Believing Without Proof

Every chapter in this book so far has been an argument. Pascal begins by conceding that they do not work.

Reason cannot settle whether God exists. He grants this before he starts, which is a striking thing for a mathematician of his standing to do, and it is what makes the wager interesting rather than merely clever. He is not adding another proof to a pile that has failed. He is asking what to do given that the pile has failed.

And his first move is the one everything else depends on.

You must wager. You are embarked.

Not deciding is not available. You will live one way or the other, and the person who suspends judgement is living the life of somebody who does not believe. Neutrality is a position, it just does not announce itself as one.

Then the structure.

If you believe and you are right, the gain is unlimited. If you believe and you are wrong, you have lost some pleasures and some time. If you disbelieve and you are right, you have gained some pleasures and some time. If you disbelieve and you are wrong, the loss is unlimited.

Look at the shape rather than the theology. One side has a bounded gain and a bounded loss. The other has an unbounded gain and an unbounded loss. When one outcome is infinite, the probability stops mattering to the calculation: any non-zero chance multiplied by an infinite payoff dominates any finite quantity.

So believe. Not because it is true, which Pascal has already said cannot be established, but because it is the rational bet.

The objections are good, and there are two that matter.

The first is that you cannot believe something by deciding to. Belief is not under voluntary control; try deciding right now that it is raining. Pascal knew this perfectly well, and his answer is the most interesting part of the argument: act as though you believed, keep the company of believers, follow the practices, and belief will follow. Behaviour shapes conviction rather than the other way round.

That is a substantial claim about human psychology, made in the seventeenth century, and it is broadly what we now think is true.

The second objection is harder. The wager works equally well for any faith that promises an infinite reward, and those faiths are incompatible with one another. The argument tells you to bet and cannot tell you what to bet on, and you cannot hedge by taking all of them.

That objection is generally taken to be fatal to the wager as an argument for any particular religion, and it leaves the structure intact.

Which is where this chapter ends up being about more than religion.

Pascal is doing decision theory under uncertainty several centuries before it had a name. Any argument of the form the probability is low, the downside is catastrophic, and the cost of precaution is bounded, so act, has exactly this shape.

You will find it in insurance, in climate policy, in pandemic preparedness and in most of safety engineering. It is one of the few genuinely load-bearing pieces of reasoning in this library, and it was invented by a man trying to work out what to do about a question he had just admitted he could not answer.