Pascal's Wager (or Pascal's Gambit) is the application by the French philosopher Blaise Pascal of decision theory to the belief in God. It was set out in the Pensées, a posthumously published collection of notes made by Pascal towards his unfinished treatise on Christian apologetics.
The Wager posits that it is a better "bet" to believe that God exists than not to believe, because the expected value of believing (which Pascal assessed as infinite) is always greater than the expected value of not believing. In Pascal's assessment, it is inexcusable not to investigate this issue:
Before entering into the proofs of the Christian religion, I find it necessary to point out the sinfulness of those men who live in indifference to the search for truth in a matter which is so important to them, and which touches them so nearly.
Variations of this argument may be found in other religious philosophies, such as Islam, and Hinduism . Pascal's Wager is also similar in structure to the precautionary principle.
The Wager is described by Pascal in the 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" or "knowledge", and our "will" or "happiness". Since reason cannot decide the issue, and both options are equally unfounded in reason, we should decide it according to our happiness. This is accomplished by weighing the gain and loss in believing that God exists. 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. 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.
Pascal recognizes that the wagerer is risking something, namely his life on earth, by devoting it to one cause or another, but here he uses probabilistic analysis to show that it would be a wise wager, at the even odds he assumes, even if one were to gain only three lives at the risk of losing one. Considering that everyone is forced to wager and the potential gain is actually infinite life, it would be acting "stupidly" not to wager that God exists.
The possibilities defined by Pascal's Wager can be expanded more fully, though it should be noted that Pascal did not address the last two possibilities explicitly in his account, nor did he mention hell.
- You live as though God exists.
- If God exists, you go to heaven: your gain is infinite.
- If God does not exist, you gain nothing and lose nothing.
- You live as though God does not exist.
With these possibilities, and the principles of statistics, Pascal attempted to demonstrate that the only prudent course of action is to live as if God exists. It is a simple application of game theory (to which Pascal had made important contributions).
Another way of portraying the Wager is as a decision under uncertainty with the values of the following decision matrix:
| 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) or −∞ (hell)) | +N (none) |
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.
