Pascal's Wager

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Pascal's Wager is a philosophical argument that originates with Blaise Pascal and attempts to give one prudential reasons to believe in God. The Wager is as follows:

If you believe in God and God exists, you get an infinite reward in the afterlife (Heaven). If you believe in God and God does not exist, you pay a small price in this life (attending church etc.). If you do not believe in God and God does not exist, you do not pay the small price that the mistaken believer pays. If you do not believe in God and God does exist, you get infinite punishment (Hell). Given the risk of being wrong, it is far more sensible to believe than not believe in God. As Pascal put it:

if you gain, you gain all; if you lose, you lose nothing. Wager, then, without hesitation that He is.

One can put this into a decision matrix, as in game theory:

Pascal's Wager decision matrix
  God exists God does not exist
Believe in God Gain everything Nil
Do not believe in God Infinite punishment Nil

The existence of multiple religions prompts some into suggesting that the matrix should not be limited to only God existing and God not existing, but has to include many conceptions of God and many proposed schemes of salvation. This involves extending the matrix in both directions. You may believe in God but not, say, the doctrines of Christianity, and God gives infinite punishment to non-Christians. You may believe in the Christian God, but the God will only save Muslims.

If God exists, there may be a scheme of salvation that differs from the one presumed by the Wager. Perhaps God has given human beings life in order so they can test their epistemic faculties and reasoning ability, and if they decide to believe in him solely because of prudential reasoning, he will consign one to hell. Perhaps God is only interested in moral deeds rather than epistemic ones. The doctrine of predestination may be in effect, and so no amount of worship or belief will change one's ultimate destination in the afterlife.

The wager presumes some form of doxastic voluntarism - that is, it presumes that one can change one's theological beliefs for prudential reasons alone. Many strongly dispute that you can do this - they accept the terms of the wager, but deny that you can have any voluntary choice in one's beliefs about God or even one's basic epistemic framework.