Philosophical Problems January 11, 2015 Pascal's Wager

Belief and Evidence If you try to drop a basketball into a large box, you should believe you'll succeed. Most people complete that 'task' successfully almost every time.

Belief and Welfare If you try to hit a free throw in a basketball game, you should believe you'll succeed. People who are confident are more likely to succeed at tasks like this.

Belief and Welfare What are some other examples where belief, against the evidence, might have good consequences?

What you should believe It feels like there are two different kinds of reasons to believe. – Truth directed – Welfare directed

Belief in God There are famously a number of truth directed reasons to believe in God. – Causal – Explanatory – Ontological Some theologians think these are all bad, and you should have faith.

Welfare and God If you believe, you'll go to heaven. If you don't, you'll go to hell. Heaven >>> Hell. So you should believe.

Blaise Pascal Lived Great mathematician A founder of contemporary probability theory Wrote on religious issues later in life

Acts and States A simple decision problem has two parts. – Acts – States The acts are the choices that are open to the agent. The states are the way the world might be.

Outcomes The outcome for the agent is a function of: – The actual state of the world – The choice she makes We represent outcomes with numbers. – Higher numbers are better. – Think of these numbers as being kinda like dollars.

Pascal's Decision Table We need to convert this to numbers to get a real table.

How good is heaven? A day in heaven has at least some positive value. There are infinitely many days in heaven. So, heaven has infinite value.

Declining marginal value A cup of coffee has at least some positive value. But the value goes down cup by cup. In principle heaven could be like that. But it seems unlikely. Let's grant: heaven = infinite utility.

Pascal's Decision Table

Theism and Unbelievers Here's a deep theological question. What happens to unbelievers if there is a God? If they go to hell, that square should get negative infinite value. But that's controversial. Let's assume they just die.

What if there's no God? Which outcome is better - theism or atheism? Let's simplify and assume that we care about two things: – Happiness – Truth

What if there's no God? If there isn't a God, atheists are doing better by the truth standard. But who does better by the happiness standard? From the armchair, I'd have guessed the atheists. As far as I can tell from the empirical work, this isn't in general true. – Theists have lots of social connections. – Possibly theists also less stressed in some ways.

Pascal's Own View This assumes theists are happier, and this balances the truth gain

Dominance Argument So theism could make things better, and couldn’t make things worse.

Dominance Argument That seems like the practical considerations strongly favor theism.

Dropping Pascal’s Assumption Assume one point for truth. And assume atheists are happier in this world.

General rule for choosing Assume have to choose between A and B. If some proposition, call it p, is true, then A is y units better than B. If p is false, then B is z units better than A. Rule: Do A just in case:

Heaven is Infinitly Good As long as probability that God exists is greater than 0, betting on God will win. Infinity times positive probability is greater than a finite gain times any probability. So become a theist!

Is This a Persuasive Argument? A. Yes B. No

For those who said No Why not? Reductionist Unfair God Many Gods Wrong Reason Puzzles about Infinity Why wait?

Can You Do It? Changing beliefs isn't like changing socks. You can't just will yourself to believe that Michigan is warm in winter. Belief isn't voluntary. And decision theory, which is what Pascal basically invented for his argument, seems to apply to voluntary acts.

The Hanging Out Solution Pascal thought about this one. He thought we should decide to hang around believers and do as they do and hope that belief would follow.

A quote Learn from those who were bound like you, and who now wager all they have. These are the people who know the way you wish to follow, and who are cured of the illness of which you wish to be cured. Follow the way by which they began: they acted as if they believed, took holy water, had masses said, etc. This will make you believe naturally and mechanically.

Infectious Beliefs What are some cases where belief is infectious?

The Theological Objection God wouldn’t let you into heaven if you believed in Him for this reason. This was stressed by William James, who was generally sympathetic to pragmatic arguments. Pascal doesn’t have much of a response to this argument.

Another Objection QI on Pascal’s Wager

Atheists Go To Heaven How is this an objection to Pascal? It suggests the table is wrong. We don't know the payoff for (atheism, God exists) is low. Although if the truth consideration is as important as Mitchell says, maybe we do know.

Many Gods Pascal wasn't just a theist, he was a Catholic. And he wasn't just a Catholic, he was a Jansenist. How do we get anything more precise out of the argument? Should it bother Pascal if we can’t?

Many Gods But will all theists go to heaven? If the argument is just an argument for monotheism, maybe only one very small subset of theists will go. Perhaps you have to please a majority of Gods to get into heaven, and all monotheists are out.

The Many Gods 'Objection' Again, how is what I just said an objection? Perhaps it suggests the big infinite value in the top left is wrong. We don't know that value is infinite, since you might pick the wrong religion.

There is More to Say! There is always more to say. Should the Many Gods objection worry Pascal? Should he be happy if he only gets an argument against atheism? Should we ever accept non truth directed arguments for the truth of a claim?

For Next Time Zeno Don’t go anywhere!