Experiment #65 · Thought experiment

Pascal's Wager

Decision-theoretic theism

Blaise Pascal · 1670 (posthumous) · Philosophy of religion, decision theory

First published: B. Pascal, *Pensées* (posthumous, 1670), §233 (Brunschvicg).

If God exists, belief yields infinite reward and disbelief infinite loss. Even tiny credence in God's existence makes belief the rational bet.

Pascal argues that under uncertainty about God's existence, the asymmetric payoffs (infinite reward for belief if God exists; finite cost if God doesn't) make belief the dominant rational strategy. The argument is the first sustained application of expected-utility reasoning to a philosophical question. Standard objections: the many-gods problem (which God to bet on?), the sincerity problem (can belief be chosen?), and the infinity problem (expected utilities with infinite payoffs misbehave). The case remains the founding case study for decision theory under deep uncertainty.

Formulation

States: God exists (probability p), God doesn't (1−p). Acts: believe, disbelieve. Payoff (believe | God): +∞. (disbelieve | God): −∞ (or large finite loss). (believe | ~God): small cost. (disbelieve | ~God): small gain. For any p > 0, expected utility of believe = +∞. Bet on God.

Compare this experiment

Dimensions Engaged

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Observer

Engages Observer · Knowledge Extent under uncertainty: how should one act when key facts are inaccessible?

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Time

Concerns Time · Extent: infinite payoffs (eternal life, eternal damnation) are central to the argument.

Responses — How Schools Engage

Denies / rejects the premise 4

Reformed / Calvinist Theology

Saving faith is the work of the Holy Spirit, not a calculated wager. Pascalian belief is at best a precursor; at worst a substitute that distracts from regeneration.

Logical Positivism

Talk of infinite payoffs in unverifiable afterlives is meaningless under the verification principle. The wager treats theology as if it were insurance.

Naturalism

The many-gods problem dispatches the wager: symmetric reasoning produces opposing bets for incompatible religions. Decision theory cannot bootstrap evidence.

Existentialism

Faith is a leap into a particular existence, not a hedge against eternal outcomes. The wager misdescribes both faith and the self that takes it up.

Reframes the question 2

Catholic/Thomistic

A useful pre-evangelical preparation but not a substitute for genuine assent; faith and the will's assent under grace, not mere expected-utility calculation, are the proper response to revelation.

Pragmatism

James' "Will to Believe" preserves a pragmatic version: in cases of forced live options where evidence is balanced, one may legitimately let one's passional nature decide. Pascal too narrowly framed.