Pascal's wager


Pascal's wager is an argument in philosophy presented by the seventeenth-century French philosopher, theologian,
mathematician and physicist, Blaise Pascal. It posits that humans bet with their lives that God either exists or does not.
Pascal argues that a rational person should live as though God exists and seek to believe in God. If God does not actually exist, such a person will have only a finite loss, whereas if God does exist, he stands to receive infinite gains and avoid infinite losses.
Pascal's Wager was based on the idea of the Christian God, though similar arguments have occurred in other religious traditions. The original wager was set out in Pascal's posthumously published Pensées, an assembly of previously unpublished notes.
Historically, Pascal's wager was groundbreaking because it charted new territory in probability theory, marked the first formal use of decision theory, existentialism, pragmatism, and voluntarism.

The wager

The wager uses the following logic :
Pascal asks the reader to analyze humankind's position, where our actions can be enormously consequential, but our understanding of those consequences is flawed. While we can discern a great deal through reason, we are ultimately forced to gamble. Pascal cites a number of distinct areas of uncertainty in human life:
CategoryQuotation
Uncertainty in allThis 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 purposeFor 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 reasonThere is nothing so conformable to reason as this disavowal of reason.
Uncertainty in scienceThere is no doubt that natural laws exist, but once this fine reason of ours was corrupted, it corrupted everything.
Uncertainty in religionIf 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 skepticismIt is not certain that everything is uncertain.

Pascal describes humanity as a finite being trapped within an incomprehensible infinity, briefly thrust into being from non-being, with no explanation of "Why?" or "What?" or "How?" On Pascal's view, human finitude constrains our ability to achieve truth reliably.
Given that reason alone cannot determine whether God exists, Pascal concludes that this question functions as a coin toss. However, even if we do not know the outcome of this coin toss, we must base our actions on some expectation about the consequence. We must decide whether to live as though God exists, or whether to live as though God does not exist, even though we may be mistaken in either case.
In Pascal's assessment, participation in this wager is not optional. Merely by existing in a state of uncertainty, we are forced to choose between the available courses of action for practical purposes.

Explanation

The Pensées passage on Pascal's wager is as follows:
Pascal begins by painting a situation where both the existence and non-existence of God are impossible to prove by human reason. So, supposing that reason cannot determine the truth between the two options, one must "wager" by weighing the possible consequences. Pascal's assumption is that, when it comes to making the decision, no one can refuse to participate; withholding assent is impossible because we are already "embarked", effectively living out the choice.
We only have two things to stake, our "reason" and our "happiness". Pascal considers that if there is "equal risk of loss and gain", then human reason is powerless to address the question of whether God exists. That being the case, then human reason can only decide the question according to possible resulting happiness of the decision, weighing the gain and loss in believing that God exists and likewise in believing that God does not exist.
He points out that if a wager were between the equal chance of gaining two lifetimes of happiness and gaining nothing, then a person would be a fool to bet on the latter. The same would go if it were three lifetimes of happiness versus nothing. He then argues that it is simply unconscionable by comparison to betting against an eternal life of happiness for the possibility of gaining nothing. 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. On the other hand, if you bet against God, win or lose, you either gain nothing or lose everything. You are either unavoidably annihilated or miss the opportunity of eternal happiness. In note 194, speaking about those who live apathetically betting against God, he sums up by remarking, "It is to the glory of religion to have for enemies men so unreasonable..."

Inability to believe

Pascal addressed the difficulty that 'reason' and 'rationality' pose to genuine belief by proposing that "acting as if believed" could "cure of unbelief":

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.

God exists God does not exist
Belief +∞ −c
Disbelief −∞ +c


Given these values, the option of living as if God exists dominates the option of living as if God does not exist, 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 results in as being the only rational decision.

God exists God does not exist
Belief +∞f1
Disbelief f2f3

Misunderstanding of the wager

Many criticisms have explained that the wager has been used as a supposed theory of the necessity to believe, although that was never Pascal's intention. As Laurent Thirouin writes:
To be put at the beginning of Pascal's planned book, the wager was meant to show that logical reasoning cannot support faith or lack thereof, Pascal's intended book was precisely to find other ways to establish the value of faith, an apology for the Christian faith.

Criticism

Criticism of Pascal's Wager began in his own day, and came from both atheists, who questioned the "benefits" of a deity whose "realm" is beyond reason, and the religiously orthodox, who primarily took issue with the wager's deistic and agnostic language. It is criticized for not proving God's existence, the encouragement of false belief, and the problem of which religion and which God should be worshipped.

Failure to prove the existence of God

, a generation after Pascal, rejected the idea that the wager was "proof of God" as "indecent and childish", adding, "the interest I have to believe a thing is no proof that such a thing exists". Pascal, however, did not advance the wager as a proof of God's existence but rather as a necessary pragmatic decision which is "impossible to avoid" for any living person. He argued that abstaining from making a wager is not an option and that "reason is incapable of divining the truth"; thus, a decision of whether to believe in the existence of God must be made by "considering the consequences of each possibility".
Voltaire's critique concerns not the nature of the Pascalian wager as proof of God's existence, but the contention that the very belief Pascal tried to promote is not convincing. Voltaire hints at the fact that Pascal, as a Jansenist, believed that only a small, and already predestined, portion of humanity would eventually be saved by God.
Voltaire explained that no matter how far someone is tempted with rewards to believe in Christian salvation, the result will be at best a faint belief. Pascal, in his Pensées, agrees with this, not stating that people can choose to believe, but rather that some cannot believe.
As Étienne Souriau explained, in order to accept Pascal's argument, the bettor needs to be certain that God seriously intends to honour the bet; he says that the wager assumes that God also accepts the bet, which is not proved; Pascal's bettor is here like the fool who seeing a leaf floating on a river's waters and quivering at some point, for a few seconds, between the two sides of a stone, says: "I bet a million with Rothschild that it takes finally the left path." And, effectively, the leaf passed on the left side of the stone, but unfortunately for the fool Rothschild never said "I bet".

Argument from inconsistent revelations

Since there have been many religions throughout history, and therefore many conceptions of God, some assert that all of them need to be factored into the wager, in an argumentation known as the argument from inconsistent revelations. This, its proponents argue, would lead to a high probability of believing in "the wrong god", which, they claim, eliminates 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."
Another version of this objection argues that for every religion that promulgates rules, there exists another religion that has rules of the opposite kind. If a certain action leads one closer to salvation in the former religion, it leads one further away from it in the latter. Therefore, the expected value of following a certain religion could be negative. Or, one could also argue that there are an infinite number of mutually exclusive religions, and that the probability of any one of them being true is zero; therefore, the expected value of following a certain religion is zero.
Pascal considers this type of objection briefly in the notes compiled into the Pensées, and dismisses it as obviously wrong and disingenuous:
This short but densely packed passage, which alludes to numerous themes discussed elsewhere in the Pensées, has given rise to many pages of scholarly analysis.
Pascal says that unbelievers who rest content with the many-religions objection are people whose skepticism has seduced them into a fatal "repose". If they were really bent on knowing the truth, they would be persuaded to examine "in detail" whether Christianity is like any other religion, but they just cannot be bothered. Their objection might be sufficient were the subject concerned merely some "question in philosophy", but not "here, where everything is at stake". In "a matter where they themselves, their eternity, their all are concerned", they can manage no better than "a superficial reflection" and, thinking they have scored a point by asking a leading question, they go off to amuse themselves.
As Pascal scholars observe, Pascal regarded the many-religions objection as a rhetorical ploy, a "trap" that he had no intention of falling into. If, however, any who raised it were sincere, they would want to examine the matter "in detail". In that case, they could get some pointers by turning to his chapter on "other religions".
As David Wetsel notes, Pascal's treatment of the pagan religions is brisk: "As far as Pascal is concerned, the demise of the pagan religions of antiquity speaks for itself. Those pagan religions which still exist in the New World, in India, and in Africa are not even worth a second glance. They are obviously the work of superstition and ignorance and have nothing in them which might interest 'les gens habiles' ". Islam warrants more attention, being distinguished from paganism by its claim to be a revealed religion. Nevertheless, Pascal concludes that the religion founded by Mohammed can on several counts be shown to be devoid of divine authority, and that therefore, as a path to the knowledge of God, it is as much a dead end as paganism. Judaism, in view of its close links to Christianity, he deals with elsewhere.
The many-religions objection is taken more seriously by some later apologists of the wager, who argue that, of the rival options, only those awarding infinite happiness affect the wager's dominance. In the opinion of these apologists "finite, semi-blissful promises such as Kali's or Odin's" therefore drop out of consideration. Also, the infinite bliss that the rival conception of God offers has to be mutually exclusive. If Christ's promise of bliss can be attained concurrently with Jehovah's and Allah's, there is no conflict in the decision matrix in the case where the cost of believing in the wrong conception of God is neutral, although this would be countered with an infinite cost in the case where not believing in the correct conception of God results in punishment.
Furthermore, ecumenical interpretations of the wager argue that it could even be suggested that believing in a generic God, or a god by the wrong name, is acceptable so long as that conception of God has similar essential characteristics of the conception of God considered in Pascal's wager. Proponents of this line of reasoning suggest that either all of the conceptions of God or gods throughout history truly boil down to just a small set of "genuine options", or that if Pascal's wager can simply bring a person to believe in "generic theism", it has done its job.
Pascal argues implicitly for the uniqueness of Christianity in the wager itself, writing: "If there is a God, He is infinitely incomprehensible...Who then can blame the Christians for not being able to give reasons for their beliefs, professing as they do a religion which they cannot explain by reason?"

Argument from inauthentic belief

Some critics argue that Pascal's wager, for those who cannot believe, suggests feigning belief to gain eternal reward. This would be dishonest and immoral. In addition, it is absurd to think that God, being just and omniscient, would not see through this deceptive strategy on the part of the "believer", thus nullifying the benefits of the wager.
Since these criticisms are concerned not with the validity of the wager itself, but with its possible aftermath—namely that a person who has been convinced of the overwhelming odds in favor of belief might still find himself unable to sincerely believe—they are tangential to the thrust of the wager. What such critics are objecting to is Pascal's subsequent advice to an unbeliever who, having concluded that the only rational way to wager is in favor of God's existence, points out, reasonably enough, that this by no means makes him a believer. This hypothetical unbeliever complains, "I am so made that I cannot believe. What would you have me do?" Pascal, far from suggesting that God can be deceived by outward show, says that God does not regard it at all: "God looks only at what is inward." For a person who is already convinced of the odds of the wager but cannot seem to put his heart into the belief, he offers practical advice.
Explicitly addressing the question of inability to believe, Pascal argues that if the wager is valid, the inability to believe is irrational, and therefore must be caused by feelings: "your inability to believe, because reason compels you to and yet you cannot, from your passions." This inability, therefore, can be overcome by diminishing these irrational sentiments: "Learn from those who were bound like you.... 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?"
Some other critics have objected to Pascal's wager on the grounds that he wrongly assumes what type of epistemic character God would likely value in his rational creatures if he existed.

Variations and other wager arguments

Since at least 1992, some scholars have analogized Pascal's Wager to decisions about catastrophic climate change. Two differences from Pascal's Wager are posited regarding climate change: first, climate change is more likely than Pascal's God to exist, as there is scientific evidence for one but not the other. Secondly, the calculated penalty for unchecked climate catastrophe would be large, but is not generally considered to be infinite. Magnate Warren Buffett has written that climate change "bears a similarity to Pascal's Wager on the Existence of God. Pascal, it may be recalled, argued that if there were only a tiny probability that God truly existed, it made sense to behave as if He did because the rewards could be infinite whereas the lack of belief risked eternal misery. Likewise, if there is only a 1% chance the planet is heading toward a truly major disaster and delay means passing a point of no return, inaction now is foolhardy."