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Pascal’s Wager on the existence of God

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(Blaise Pascal)

Pascal’s wager is a philosophical argument developed by Blaise Pascal, a 17th-century French philosopher, mathematician, and physicist. The argument tries to prove that a rational person has every interest in believing in God, whether God exists or not. Indeed, if God does not exist, the believer and the non-believer lose nothing or almost. On the other hand, if God exists, the believer wins paradise while the non-believer is locked up in hell for eternity.

The original text of the bet is found in a fragment (Lafuma 418 – Brunschvicg 233) of the Pensées, a work defending the Christian religion against skeptics and free thinkers.

Excerpt from Pensées

“Let us examine this point, then, and say, ‘God exists, or he does not exist. But which way shall we lean? Reason can determine nothing about it: there is an infinite chaos that separates us. A game is being played, at the end of this infinite distance, where a cross or a tail will come up. What will you bet? By reason, you cannot do either; for good reason, you can’t undo either of them. So do not blame falsehood on those who have taken a choice; because you know nothing about it. – No ; but I will blame them for having made, not this choice, but a choice; for though he who takes the cross and the other are in like fault, they are both in fault: it is just not to bet. “Yes, but you have to bet; this is not voluntary, you are on board. So which will you take? Let’s see. Since you have to choose, let’s see what interests you the least. (…). Your reason is not hurt any more by choosing one than the other, since it is necessary to choose. This is an empty point. But your bliss? Weigh the gain and loss, taking the cross that God exists. Let’s estimate these two cases: if you win, you win everything; if you lose, you lose nothing. Bet therefore that he exists, without hesitation. »
—Blaise Pascal, Pensées, fragment 397.


For Pascal, there are only two possibilities: either God exists or God does not exist. However, our reason is unable to determine which of these two propositions is true. Pascal, however, believes that one should not suspend judgment and become agnostic. On the contrary, he believes that believing in God is more advantageous than not believing in him. The reason behind this last statement can be understood if we compare human life to a game of chance in which you have the opportunity to bet on the existence of God. Since you don’t know whether God exists or not, you find yourself in the same situation as a bettor before the start of a race. To determine the most advantageous bet, you must determine what you have to lose and what you have to gain.

The question then is what do you have to gain and what do you have to lose in this bet on the existence of God. For Pascal, the answer is quite simple. First, suppose you bet on the existence of God. There are two possibilities: either you got it wrong and God doesn’t exist, or he really does. If he doesn’t exist, you will have lost almost nothing. On the other hand, if he exists and you believed in it, you will get a spectacular reward since you will be rewarded with an eternity of happiness in paradise. Now let’s take the other case: you’re betting that God doesn’t exist. Again there are two possibilities: either you are right and it doesn’t exist, or it really does exist. The outcome of the game, however, is vastly different. Indeed, if it does not exist; you may have been able to enjoy life more freely because you didn’t have to follow religious rules. On the other hand, if it exists, the result is dramatic. You will indeed be condemned to remain locked up in hell forever and to undergo infinite suffering there.

Consequently, according to Pascal, we have no reason to believe that God really exists but we have an interest in believing in him. Indeed, if God does not exist, the believer and the non-believer lose almost nothing. On the other hand, if God exists, the believer wins everything, that is to say paradise, while the non-believer goes to hell for eternity. It is therefore more advantageous to believe in God.

Presentation in the form of a table

The possible gains and losses can also be represented in the form of a table.

  1. If you bet on the existence of God and God does not exist, you experience a loss (for atheists, forced to respect a religious morality) or a gain (for theists, finding comfort in religion), in both cases finished.
  2. If you bet on the existence of God and that God exists, your gain is infinite. You experience eternal happiness in paradise.
  3. If you bet against the existence of God and God does not exist, you obtain a loss or a finite gain inverse to that of 1, depending on whether you are atheist or theist.
  4. If you bet against the existence of God and that God exists, your loss is infinite. You are locked up for eternity in hell.

Mathematically, a finite loss or gain is negligible compared to an infinite loss or gain. Indeed, if you bet on the existence of God, the worst that can happen to you is to have had to respect the religious rules for nothing. On the other hand, you have a certain chance of gaining paradise. In the other case, if you are betting against the existence of God, the best that can happen to you is to have enjoyed a life where you have not bothered with religious rules. However, the worst that can happen to you is to burn in hell for eternity. Consequently, it is far better to believe in God than not to believe in him.

God exists God does not exist
You bet on the existence of God You go to heaven = you win forever (+∞) You return to nothingness = you suffer a finite loss or gain (f1)
You bet on the non-existence of God You burn in hell = you lose indefinitely (−∞) You return to nothingness = you get a finite gain or loss (f2)

Critics of wager

Gambling may displease God

It is also necessary to consider that the personal advantage is a reason to believe in God which can turn against the bettor. Indeed, God, being hypothetically omniscient, will know if the bettor has led the life of a believer out of self-interest. It is then possible that he considers the gambler’s motivation to be inadequate and that he decides to punish him with eternal damnation rather than reward him with eternal bliss. It should however be noted that Pascal was aware of the problem and that he considered his bet as making it possible to take a first step towards a more authentic faith. The purpose of the argument of the bet was not to convince the reader to opt for the Christian religion, but rather to cause in him an awareness so that he frees himself from the hold that his earthly habits.

Multiple Gods objection

Pascal seems to assume that there is only one God, the Catholic God. The problem seems to be that there are or have been multiple conceptions of God and the probability of their existence cannot be neglected in the bet. The question then arises as to how one should bet. At first sight it seems rational to believe in all gods. But this is impossible because many religions precisely require not to believe in other gods. Diderot expresses the argument succinctly, writing: “Pascal said: ‘If your religion is false, you risk nothing by believing it true; if it is true, you risk everything by believing it false’. So, if you believe true a religion which is false, you believe false the others of which one could be true, the bet is thus always losing and Pascal was wrong.”

Belief is not a voluntary act

It can be argued that to believe or not to believe are not our choices. It is not certain that it is possible to adopt a belief simply because we decide to adopt it. If we’re offered $1,000 to believe the sky is green, it seems unlikely that we’ll be able to adopt that belief simply because it’s in our best interests. Accordingly, one could argue that Pascal’s bet does not motivate us to believe in God, because believing in God is not a voluntary act.

Include texts translated and adapted from Wikipedia

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