Pascal’s Wager

Pascal’s Wager• Blaise Pascal (1623 - 1662)

• Mathematician, Physicist,Philosopher.

• Pascal is a Theist.

Agenda• Pascal: Theism without Evidence• The God Lottery• Pascal’s Wager• Two Objections

Pascal and Evidence of God’s Existence

• Pascal is not interested in producing evidence that there is a God.

“If there is a God, He is infinitely incomprehensible, since, having neither parts nor limits, He has no affinity to us. We are then incapable of knowing either what He is or if He is. This being so, who will dare to undertake the decision of the question? Not we, who have no affinity to him.” (p. 50)

Pascal is not an Agnostic• Pascal, however, is not an agnostic. • Distinguish:

evidence for a claim; and reason to believe it.

• Examples?

If you’re gambling with your (after-)life, the smart money is on

God’s existence.

Bets and Evidence• Note: An argument that you should take a particular bet

does not provide evidence that the claim you bet on is true.

• Example: Should you pay $1 for a 1 in 7.2 million chance to win $10 million?

• Similarly, Pascal tells us that we should a certain bet that we will win if there is a God. This provides no evidence at all that God exists.

Agenda• Pascal: Theism without Evidence• The God Lottery• Pascal’s Wager• Two Objections

Some principles from Decision Theory

1. The probability of a given outcome o (pro) is a number between 0 and 1, measuring how likely o is to occur.

2. The probabilities of all possible outcomes sum to 1.3. The payoffs of atheism being true and theism being true

are affected by which doctrine I decide to believe. Call the payoff for a given course of action C if outcome o occurs: “payoff(C, o)”

4. Definition: The expected payoff of any course of action C is

Σo (pro × payoff(C, o))(i.e. the sum, for all outcomes o, of

(the probability of o × the payoff for C if o occurs.))

Jim Bakker’s Thesis

• The Payoff Principle: Among the actions available to you, you should do the one which has the highest expected payoff.

• Jim Bakker’s Thesis: The expected payoff of believing in God exceeds the expected payoff of not believing in God.

Playing the God LotterySuppose life was like this:

Outcomes Expected Payoffs

(Probability = 1 in 1 million)

God Exists God does not exist

(Probability ≈ 1)

Don’t believe

Believe

$1 billion $50

$100 $100

Should you be a theist?

LOSER!Winner! 1/1 m × $1 bn + ~1 × $50 ≈ $1,050

1/1 m × $100 + ~1 × $100 = $100

Courses of Action

You should be a Theist if you’re playing the God Lottery

• A Conclusion: If you’re playing the God Lottery, you should be a theist. [by Payoff Principle + Jim Bakker’s Thesis]

• Objection: You’re not playing the God Lottery.

Agenda• Pascal: Theism without Evidence• The God Lottery• Pascal’s Wager• Two Objections

Real Life, According to Pascal

Outcomes Expected Payoffs

(Probability = 1 in 1 million)

God Exists God does not exist

(Probability ≈ 1)

Don’t believe

BelieveThe joys of heaven for all eternity

Tithing + foregoing all of these goodies

The torments of hell for all eternity

The pleasures of the life of “license”

Should you be a theist?

Courses of Action

??

A Stubborn Fact

• The difference in how good the joys of heaven are from the torments of Hell for all eternity is at least a million times greater than the difference between how good the joys of a life of “license” are from the travails of a life of piety.

niceness of heaven)nastiness of hell-( > niceness of “license”

nastiness of piety-( )1 million ×

From Payoff to Utility• If we want a way to calculate payoffs, then

we can talk about quantities of pleasure (goodness, yumminess, etc.) that we get from our lives.

• A util is a unit of pleasure (goodness, yumminess, etc.).

Expected Utility1. Call the utility of a given course of action C if

outcome o occurs: “utility(C, o)”

2. Definition: The expected utility of any course of action C is

Σo (pro × utility(C, o))(i.e. the sum, for all outcomes o, of

(the probability of o × the utility of C if o occurs.))

The Utility PrincipleThe Utility Principle: Among the actions

available to you, you should do the one which has the highest expected utility.

Pascal’s Thesis: The expected utility of believing in God exceeds the expected utility of not believing in God.

Here’s the Wager

Outcomes Expected Utilities

(Probability = 1 in 1 million)

God Exists God does not exist

(Probability ≈ 1)

Don’t believe

Believe1 billion utils(at least)

50 Utils

100 utils(at most)

100 utils

Should you be a theist?

Courses of Action

~1,050 Utils

~100 Utils

Pascal’s Wager

1) The Utility Principle: Among the actions available to you, you should do the one which has the highest expected utility.

2) Pascal’s Thesis: The expected utility of believing in God exceeds the expected utility of not believing in God.

(C) You should believe in God.

Agenda• Pascal: Theism without Evidence• The God Lottery• Pascal’s Wager• Two Objections

Two Objections: Agenda1. “I can’t believe!”2. The Many Gods Objection

Objection: “Nice work, if you can get it.”

• Pascal is assuming: believing is like betting.

• The argument shows only that, if one could get oneself to believe that God exists, then one should.

It ain’t easy to believe.• The atheist: “I can’t take the bet!”

“Yes, but I have my hands tied and my mouth closed; I am forced to wager, and am not free. I am not released, and am so made that I cannot believe. What, then would you have me do?” (p. 51, cols. 1-2)

The Objection Stated1) The Utility Principle: Among the actions available to you,

you should do the one which has the highest expected utility.

2) Pascal’s Thesis: The expected utility of believing in God exceeds the expected utility of not believing in God.

3) Believing in God is available to you.(C) You should believe in God.

Objection:

There’s a hidden premise in the argument.

That premise is false.

Is theism completely out of our reach?

• Pascal: You can use indirect means to get yourself to believe.

“True. But at least learn your inability to believe, since reason brings you to this, and yet you cannot believe. Endeavour then to convince yourself, not by increase of proofs of God, but by the abatement of your passions. You would like to attain faith, and do not know the way; you would like to cure yourself of unbelief, and ask the remedy for it. Learn of those who have been bound like you, and who now stake all their possessions. These are people who know the way which you would follow, and who are cured of an ill of which you would be cured. Follow the way by which they began; by acting as if they believed, taking the holy water, having masses said, etc.” (p. 51, col. 2)

You’ve got a bad disease• Pascal uses an extended metaphor: Atheism

(or agnosticism) is a disease, for which you should be seeking the cure.

• Examples: cognitive behavioral therapy. You can’t just “not be

depressed.” But there are things you can do to lift your mood, and combat the undermining thoughts you have.

smoking cessation. You can’t keep living exactly the life you do and just “not smoke.” You have to take indirect steps. (I run (or I used to).)

You Can Do It! Pascal’s Prescription

• The Recommended Treatment Regimen: Act religious.

• It is Available There’s a monotheistic religious institution right around the

corner.• It is Safe

Risks of side effects: tithing, the loss of the pleasures of a life of “license”.

• It is Effective Atheists and agnostics who adhered to this regimen for decades

have shown significant improvement, and some have even gone into remission.

Two Objections: Agenda1. “I can’t believe!”2. The Many Gods Objection

The Many Gods Objection

• Pascal assumes: there are only two possible outcomes:i. God exists and rewards believers (as the

Christians describe God, more or less); orii. God does not exist.

• Note: Pascal has given us no evidence for this assumption.

Pascal’s God• Pascal claims that it is consistent with our evidence that

there turn out to be a God who rewards the faithful and punishes the nonbelievers.

• Pascal: For all we know, there is a belief-rewarding God.

An Indulgent God?• For instance, it might be, for all we know, that God exists

and is indulgent: everyone goes to heaven.

A Vengeful God?

• It also might be, for all we know, that God exists and is vengeful: everyone goes to hell.

An Anti-Monotheist God?• It also might be, for all we know, that God exists

and is opposed to his own worship.• Monotheists go to hell; Everyone else goes to

heaven.

The Many Gods Objection Stated

• Pascal has mischaracterized the betting situation.

• As a result, Pascal’s Thesis is false.

Pascal’s Thesis: The expected utility of believing in God exceeds the expected utility of not believing in God.)

The Many Gods Counter-Wager

OutcomesExpected Utilities

(Prob = 1 in 1 million)

Pascal’sGod Exists

No Godexists

(Prob ≈ 1)

Don’t believe

Believe1 billion utils(at least)

50 Utils

100 utils(at most)

100 utils

Should you be a theist?

Courses of Action

~1,050 Utils

~1,100 Utils

Anti-Mono.God Exists

(Prob = 1 in 1 million)

1 billion utils(at least)

50 Utils