# Pascal's Wager

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Blaise Pascal argued that it is a better "bet" to believe in God than not to do so.

Pascal's Wager (also known as Pascal's Gambit) is Blaise Pascal's application of decision theory to the belief in God. It is one of three 'wagers' which appear in his Pensées, a collection of notes for an unfinished treatise on Christian apologetics. Pascal argues that it is always a better "bet" to believe in God, because the expected value to be gained from believing in God is always greater than the expected value resulting from non-belief. Note that this is not an argument for the existence of God, but rather one for the belief in God. Pascal specifically aimed the argument at such persons who were not convinced by traditional arguments for the existence of God. With his wager he sought to demonstrate that believing in God is advantageous to not believing, and hoped that this would convert those who rejected previous theological arguments.

Variations of this argument can be found in other religious philosophies, such as Hinduism.

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## Explanation

It states that if you were to analyse your options in regard to belief in Pascal's God carefully (or belief in any other religious system with a similar reward and punishment scheme), you would come out with the following possibilities:

• You may believe in God, and God exists, in which case you go to heaven.
• You may believe in God, and God doesn't exist, in which case you gain nothing.
• You may not believe in God, and God doesn't exist, in which you gain nothing again.
• You may not believe in God, and God may exist, in which case you will be punished.

From these possibilities, and the principles of statistics, Pascal deduced that it would be better to believe in God unconditionally. It is a classic application of game theory to itemize options and payoffs and is valid within its assumptions.

The following table shows the values that Pascal assigned to each possible outcome:

 God exists (G) God does not exist (~G) + ∞ (heaven)
0 − ∞ (hell) 0

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Given the values that Pascal proposes, the option of believing in God (B) dominates the option of not believing in God (~B). In other words, the value gained by choosing B is always greater than or equal to that of choosing ~B.

At first, Pascal assigns equal probability to each of the two possibilities. He argues that "reason is no more shocked in choosing one rather than the other," due to our ignorance. However, he later points out that the probabilities make no difference to the argument, since any non-zero chance multiplied by infinity yields an infinite expected value.

Pascal's Wager is similar in structure to the Precautionary principle, and has similar strengths and weaknesses.

## Criticisms of Pascal's Wager

Before entering into the criticisms of the Wager, it is only fair to note, as is less widely known, that the wager was never intended to be a basis or reason for faith. The wager is found in an apologetic (his Pensées) aimed at those who didn't consider the question of God worth considering. The wager had the express intention of showing the "happy agnostic" the value and probable necessity of considering the question of God.

Pascal has been severely criticized, for example by Voltaire. Some criticisms are summarized below:

### Assumes God rewards Belief

Pascal's wager suffers from the logical fallacy of the false dilemma, relying on the assumption that the only possibilities are:

1. the Christian God exists and punishes or rewards as stated in Christian theology, or
2. no God exists.

The wager does not account for the possibility that there is a God who, rather than behaving as stated in certain parts of the Bible, instead rewards skepticism and punishes blind faith, or rewards honest reasoning and punishes feigned faith.

Also, in the many human societies where belief in a particular religion is rewarded by economic and social benefits, the wager permits the hidden addition of such benefits to the wager, and many memeticists (those who work with concept of the meme) believe that this forms much of the unconscious core of religious belief.

### Assumes a Christian God

The "many-gods" argument points out that we can find indefinitely many other possibilities offering eternal bliss and threatening eternal torment. For example, non-Christian gods might exist, and punish Christian believers for their failure to believe in them. Or some powerful entity might decide to punish those who believe in a god while rewarding non-believers. Even if (contrary to Pascal's original argument) we can assign greater probability to one of the possible outcomes, it makes no mathematical difference. As the previous section mentions, any non-zero probability multiplied by infinity yields an infinite expected value.

In this way, Pascal's Wager can be used to deduce that it is advisable to believe in any or all of a variety of gods; however, the belief systems of most religions require exclusive belief in the god of that religion, so the wager is simply not valid when applied to such religions. This is the solecism known as the argument from inconsistent revelations, though not all religions (for example, Sanathana Dharma and Pantheism) suffer from it. There is also the Jewish faith to consider, which expects a non-Jew only to obey the Noachide Laws in order to receive reward in afterlife. In addition, some religions do not require a focus on a deity, such as Buddhism. A "many-gods" version of Pascal's Wager is reported by the 13th century Persian chronicler Ibn Rustah to have been taken by a king in the Caucasus, who observed Muslim, Jewish and Christian rites equally, declaring that "I have decided to hedge my bets".

### Statistical arguments

The wager fails to mention any costs relating to belief. It is argued that there may be both direct costs (time, health, wealth) and opportunity costs. Most modern religions require their followers to spend time attending religious services at temples and to donate money to these temples when possible so that they can be maintained. As a result, if a person believes in a God that does not exist, then that person has lost time and money that could have been used for some other purpose. There may be opportunity costs for those who choose to believe: for example, scientific theories such as evolution that appear to some to contradict scripture could theoretically enable a non-believer to discover things and accomplish things the creationist could not. It is also argued that belief incurs a cost by not allowing the believing person to participate in and enjoy actions forbidden by dogma. Many devout people make more noticeable sacrifices for their religious beliefs. For example, Jehovah's Witnesses do not accept blood transfusions. If a Jehovah's Witness's death could have been prevented by a blood transfusion, and there is no God, then the Jehovah's Witness has lost his or her life needlessly.

The wager assumes a non-zero chance that God exists. This makes it ineffective on strong atheism which assigns the chance that God exists to zero, making choosing to believe or not believe provide an equal reward (0). Others have argued that the utility of salvation cannot be infinite, either via strict finitists or belief that an infinite utility could only be finitely enjoyed by finite humans.

### Many way tie

Although many people, even those highly critical of the Wager, have conceded that it is logically valid, some have argued that it is not. Given that the choice of wagering has an infinite return, then under a mixed strategy the return is also infinite. Flipping a coin and taking the wager based on the result would then have an infinite return, as would the chance that after rejecting the wager you end up taking it after all. The choice would then not be between zero reward (or negative infinite) and infinite reward, but rather between different infinite rewards.

### Assumes one can choose belief

The wager may also be criticised for requiring one to choose one's beliefs. Advocates of certain views of the nature of free will would claim that beliefs are not something that we can choose. A person who accepted the tenets of the wager might act in a pious and believing way throughout their life, but without some better reason than their own self-interest, they might not have the option to choose to believe in God.

Pascal acknowledged that there would be some difficulty for an atheist, intellectual persuaded by this argument, in putting it into effect. Belief may not come. But in such a case, he said, one could begin by acting as if it had come — hear a mass, take holy water. Belief might then follow.

There is also the argument that one could "game" the wager in a scenario where the deathbed conversion is possible — as is the case in some streams of Christianity. The person who converts on their deathbed could have failed to have been dutiful in fulfilling their doctrinal obligations, and still gain the happiness associated with the Christian concept of "heaven". The danger here is well known to most Christians, as this is a common theme of sermons in a variety of denominations. The risk of taking this gamble only to die suddenly, and without warning, or to experience the time of tribulation is often portrayed as too great a risk to take. There are also a number of Christians who disagree with the doctrine of salvation by repentance alone and that God also rewards good works. Under this assumption, Pascal's Wager is all the more important.

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