Pascal’s Wager

Posted: Mon, Mar 2, 2026

Today

• Maimonides on divine providence [35 min]
• Pascal’s wager [30 min]
• Questions on the first response paper? [save 10 min]

Epistemic vs. pragmatic reasons for belief

• Epistemic reasons for belief have the right kind of connection to truth or knowledge.
• Pragmatic reasons for belief are merely practical.

Example: Severance is a brilliant TV show.

• An epistemic reason to believe this: A lot of my friends say so, and they know what they are talking about.
• A pragmatic reason to believe this: It will make my girlfriend happy.

Pascal’s move: We have a compelling pragmatic reason to believe in God.

• Is this enough for “true” belief? [Anya, Leah, Zohia, Anika, Samantha, Megan, Lucy]

Decision under uncertainty

	Friend @ Prospect Park (25%)	Friend @ Transit Museum (75%)
Go to Prospect Park	50	25
Go to Transit Museum	25	100

Expected utility: How good/bad the outcome is expected to be.

• EU_PP = 25% × 50 + 75% × 25 = 31.25
• EU_TM = 25% × 25 + 75% × 100 = 81.25

Applied to belief in God

	God (x%)	No God (100% − x%)
Believe in God	∞	0
Don’t believe in God	−∞	0

The value of x does not matter:

• EU_Believe = x% × ∞ + (100% − x%) × 0 = ∞
• EU_{Don’t believe} = x% × −∞ + (100% − x%) × 0 = −∞

You may think there is a cost to believing in God: The argument goes through so long as the cost is not infinite.

A third row?

	God (x%)	No God (100% − x%)
Believe in God	∞	0
Wager for God	?	0
Don’t believe in God	−∞	0

Too many gods?

Can you run the argument over and over again for many, many Gods—even beyond actual world religions? [Sophie, Zi]

Omnibenevolence?

	God (x%)	No God (100% − x%)
Believe in God	∞	0
Don’t believe in God	∞	0

Naughty God?

What if God is a philosopher who wants you to believe only what you have good epistemic reasons to believe? [Zohia]

	God (x%)	No God (100% − x%)
Believe in God	−∞	0
Don’t believe in God	∞	0