Pascal’s wager

In short: Pascal’s wager is an argument by the 17th-century French mathematician and philosopher Blaise Pascal. It claims that it is reasonable to bet on the existence of God, because you have little to lose and infinitely much to gain.

In more detail: The argument does not try to prove that God exists. It is a consideration about deciding under uncertainty and is regarded as an early example of thinking in the spirit of decision theory.

In detail

• Origin: The reasoning appears in Pascal’s “Pensées” (Thoughts), a collection of notes that was only published after his death.
• The four cases: If you believe and God exists, you gain everything; if you believe and God does not exist, you lose little; if you do not believe and God exists, you lose everything; if you do not believe and God does not exist, you gain little.
• The logic behind it: Because an infinite gain outweighs any finite stake, belief appears by this calculation to be the better choice even if the probability is low.
• Expected value: Pascal also worked on the foundations of probability theory, and at its core the wager uses the idea of weighing gain against probability.
• The many-gods objection: Critics point out that there are many religions with different gods, so it remains unclear which one you should actually bet on.
• Belief on command: Another objection is that you cannot simply decide to believe something; Pascal suggested living a religious practice so that belief would develop over time.
• Sincerity of belief: Some ask whether a belief that arises from a calculation of benefit would be valuable in a religious sense at all.
• Calculating with infinity: Philosophers also discuss whether infinite values can meaningfully be used in such calculations at all.
• Relevance today: The wager is still discussed in philosophy, philosophy of religion and decision theory, whether or not one agrees with it (logik-grundlagen-schluesse, erkenntnistheorie-wissen-und-glauben, trugschluesse-erkennen).