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Pascal's Wager

The following lists a few of my favorite Pascal's Wager arguments. It states that all humans bet their lives that God either exists or doesn't.

"Blaise Pascal is a seventeenth-century French philosopher, mathematician and physicist. Pascal formulated the wager within a Christian framework. The wager was set out in section 233 of Pascal's posthumously published Pensées ("Thoughts"). These previously unpublished notes were assembled to form an incomplete treatise on Christian apologetics.

The wager uses the following logic:

  1. God is, or God is not. Reason cannot decide between the two alternatives.
  2. A Game is being played... where heads or tails will turn up.
  3. You must wager (it is not optional).
  4. 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.
  5. 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.
  6. But some cannot believe. They should then 'at least learn your inability to believe...' and 'Endeavour then to convince' themselves.
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.

There are many problems with the reasoning in Pascal's Wager, as well as the unsavory theological assumptions it makes. Like most arguments for the existence of God, it seems more about reassuring existing believers than converting non-believers. This is because in order to convince a non-believer, a theological argument must both prove that the god it argues for is the One True God and disprove all other possibilities. People lacking a belief can see the potential for multiple gods existing, in fact an infinite number, but believers are constrained by their existing view that there is their god or no god. Only in this latter case does the reasoning behind Pascal's Wager make any sense.

In Bayesian terms, this can be stated as saying non-believers attribute uniform prior probabilities to the existence of any particular god; all equal, and all infinitesimal. Pascal's Wager alone cannot update these probabilities as the reasoning applies only to the One True God out of an infinite number of possible gods. Without any further information to whittle this down, the odds of inadvertently worshiping the wrong god is a practical certainty. Only when the probability of a particular god existing increases does Pascal's Wager become useful, i.e., if one god could be assigned even a mere 1% chance of being the One True God, Pascal's Wager would present a clear benefit. Hence for anyone constrained by a bias towards a particular god, the Wager is far more clear cut and supportive of their belief.

The biggest irony of Pascal's Wager as far as Christian apologetics go is that even if it was otherwise completely sound it should then suddenly become a huge disincentive for convincing an unbiased party to worship YHWH specifically. By definition worshiping the Judeo-Christian God requires the worshipper to actively reject the existence of every other deity or potential deity thanks to the intolerance that is the First Commandment. In the absence of evidence for a specific deity, the theist-to-be would be better off directing some worship to one or more proposed deities that do not require exclusive worship. Pascal's Wager being a lynchpin of Christian apologetics (rather than being a shibboleth that must be denied at all costs) can be viewed as a case of cognitive dissonance engendered by Christian privilege.

Pascal's wager makes a number of assumptions about reality, and a number of theological assumptions about the god it argues for. If any of these can be shown to either be false or undesirable, then the power of the Wager for determining one's actions and beliefs is severely weakened - indeed, the argument of the Wager can be reversed in some cases and it can argue for non-belief. These mostly stem from the theological implications of applying the Wager to belief in God, rather than the Game Theory attributes and decision making process presented.

Pascal's wager assumes the afterlife can exist. However, all the evidence points towards a physical "person." What is the "soul" that exists after death? Such a part would have to be non-biological and non-modifiable, and no such part exists. Our thoughts, feelings, memories, and personality have been shown to come from interactions in the brain. They can also be affected by hormones, drugs, alcohol, head trauma, and other physical factors. No amount of philosophical babble can change this.
For an analogy: Let's say you (don't do this at home) dropped your computer from a 4 story building, ran over the remains 8 times, and dropped the remains in the ocean. Is the computer still running Windows in another plane of existence?

Perhaps the core of the Wager is that it assumes a human being has the ability to believe something by an act of will: not just to say one believes it but to actually, sincerely, believe it to be true. This is known as doxastic voluntarism; it is probable that most people lack the ability to do this deliberately. Beliefs are often involuntary; at the very least you (yes, you) possess an involuntary belief that you experience the world. Further, you have an involuntary belief that someone, somewhere, at some point in time, typed these very words. Similarly, it is difficult to believe things you know to be untrue. Consider how you would respond if someone told you to believe that the earth rested upon the back of a giant turtle. Even if you were inclined to, it is doubtful whether you really could genuinely believe it. Pascal attempted to "solve" this problem by saying that a nonbeliever should associate with believers, attend religious services, etc. until this inspires belief in them-essentially "fake it 'til you make it." The effectiveness of this is highly questionable though.

Freedom of action, however, is significantly different. This is something that people have considerably more free will to exert — so someone is free to worship God without believing. The question, therefore, is whether God has the ability to detect such a ruse or such belief in belief, or whether God would be happy to have people "fake" their beliefs in such a way.

Pascal's Wager must, at the very least, make one of the following assumptions:
  • That doxastic voluntarism is possible.
  • That God doesn't care if you "fake it".
One of those is known to be wrong, the other is theologically questionable.

The Wager assumes that God will be impressed by, and happily reward, people who worship just to avoid Hell. An all-powerful (or very powerful) being would gain little from the mental allegiance of human beings. In the same way, a human persuading all the inhabitants of an anthill to worship you would be pretty pointless. The constant harangues and demands for worship by the Abrahamic god as stated in the Old Testament suggest that it might just be an ego thing.

If, as Pascal's Wager must assume, God is willing to punish good people simply for a lack of belief, this would preclude God being "good" by any sense that we understand the concept of "good" - and "good" is a necessary property of God. As it can be demonstrated on Earth that no single specific religion has a monopoly on good and moral people, a God that causes Pascal's Wager to be valid cannot be focused on spreading good around the world. Various responses to Pascal's Wager involve pointing out that to be at the constant beck-and-call of such a clearly evil being would be less preferable to hell, and so it is favorable to disbelieve.

As an extension to the above, the Wager also assumes that a believer will only care about maximizing their own gains.

More troubling than this are occasions where you might theoretically be called upon to hurt someone else to advance your worship of the superior entity. This forms a flip-side to the argument that Pascal's Wager emphasizes belief over worthiness in that it suggests that outright evil people can gain reward and avoid punishment simply through belief. In the Old Testament there are numerous instances when worshipers had to kill and hurt others as commanded by God. In fact, there are occasions in which God was extremely displeased that they didn't take the abuse of fellow humans far enough. Even with the Pascal's Wager metric in place, one could argue that it's more moral to resist these commands for the sake of others even if it results in an infinite loss for you.

Again, it can be demonstrated on Earth that bad people who do bad things can still profess belief - Pascal therefore suggests they are worthy of infinite gain, and atheists cheekily suggest that being around those people in heaven isn't selling the whole belief thing to them very well.

Assuming that Pascal's Wager argues only for a Christian God (which narrows it even further from monotheistic and Abrahamic), there exists a number of sects and sub-sects that worship in different ways. Some require more stringent conditions for proper worship than others, and some of them downright contradict each other. The Wager alone doesn't really state how to get around this - presumably you just follow whatever Blaise Pascal did. So, if you don't do enough of the rituals required for proper worship you will still go to hell, not getting compensated for whatever piety-based losses you did incur.


Consider if God decided that the Mormon way of worshiping him was correct and that the Catholic way was incorrect. Then we are faced with having to believe in a God that waited for most of human history to reveal the correct way to pass the test! In fact, no matter which historical religion you choose, God has waited for most of human history to reveal the correct way to pass the test.
Alternatively, consider that none of the religions so far have it right. Behaving randomly would give you odds as good as joining any particular religion or religious sect. Indeed, since humans have no way of knowing which way is pleasing to God you may as well not even bother trying; a tiny gain plus going to Hell is better than a tiny loss plus still going to Hell.

Alternatively alternatively, consider that a previous religious did have it right in the past but then died out with no way to fully replicate their rituals. If, say, the Cathars knew the right way to get into heaven, the Albigensian Crusade pretty much permanently cut off that or any line of heavenly ascension -- thus making anyone's worship thereafter pointless.

One hidden assumption of Pascal's Wager is that the cost of worship is in fact infinitely small in some way. While this seems to be the case for limited human activities done in our mortal existence such as praying or church attendance, some religions in fact require a neverending payment in some form that will never ever be regained. This applies most notably to the Judeo-Christian religion; if the Book of Revelation is to be believed, once the elect actually ends up in Heaven they get brainwashed to worship the creator for eternity and lose a part of identity, never to be regained.

If you think that this would still be an axiomatically acceptable trade-off, ask how many people would be willing to trade an immortal existence of hedonism and pleasure in The Matrix if it meant forever being shielded from the truth. The number of people claiming that this is not a fair trade will be non-zero.

Utility is a measure of how good something is now - in economics it basically asks "how likely is someone to want it so much as to buy it". Marginal utility is a related concept that asks how this changes as you start to have more of something. Pascal's Wager and its fast-and-loose use of gains and losses is based around this concept. It assumes that going to hell will be infinitely miserable, while going to heaven would be infinitely pleasurable.

Consider that the afterlife lasts infinitely. Marginal utility states that the reward felt in the afterlife is certain to diminish over time, and that the punishment felt in hell will eventually turn from "screaming pain" to "meh" after a few million years or so - which is still tuppence compared to infinity. Therefore, on average, the marginal utility of any experiences in the afterlife are likely to be infinitesimal. Although this doesn't disprove the existence of an afterlife, it is a common argument against the desirability of an infinite afterlife and so affects the Wager's outcomes greatly. Consider a lottery payout of a million dollars... paid in installments of one dollar per year for example. Then consider a lottery payout of infinite dollars... paid in a single cent per century. The latter still gives you "infinite gain", but with a near-zero marginal utility.

This re-contextualisation quantifies the gain felt by believing in God considerably, and suggests the reward in the afterlife doesn't necessarily outweigh the finite losses felt in a mortal life.

The Bible says things like every knee shall bow, every tongue confess. It has verses that might imply annihilation rather than hell. It also claims that Yahweh is a loving god. Other religions that claim hell usually don't say things like this. So according to this wager Christians should all be Muslim because the Koran promises hell while the Bible has controversial statements about it.

Scary example:
If you ask most Christians whether children who die when they are very young will go to heaven, They will say yes. So it would be most reasonable to kill your children while young (especially since children today are much more likely to become atheists), rather than risk them leaving the Christian faith."

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