Pragmatic Arguments for Belief

Every argument in this tier so far has tried to show that theism is true, or that it is more probable than not. The arguments in this one do something different, and the difference is easy to miss because they are filed alongside the others.

They concede the point. They grant, for the sake of argument, that the evidence does not settle the question, and then ask what a person in that position should do. Not what they should conclude, which is the earlier question, but what attitude they should take up given that concluding is not available.

This is a change of subject rather than a further contribution to the old one, and keeping that in view prevents most of the confusion these arguments generate.

What kind of argument this is

Two features follow immediately, and both are frequently overlooked by people arguing about these arguments.

A pragmatic argument for theism is entirely compatible with theism being false. Nothing in it bears on the truth of the conclusion, and its most successful possible form would leave the question of God's existence exactly where it found it. Anyone who treats a wager argument as evidence has misunderstood what they are holding.

And pragmatic reasons are not disreputable in general. They are the ordinary reasons for action. It is a good reason to take an umbrella that being rained on is unpleasant, and nobody thinks this is a strange sort of reason. The difficulty is specific: whether considerations of that kind can be reasons for believing something, which is not an action and does not obviously answer to the will at all. That difficulty gets its own section below, because it is where the whole family is most vulnerable.

Pascal's wager

The passage appears in the Pensées, the collection of fragments published after Pascal's death in 1670, under a heading about infinity and nothing.

Two things about the context are worth having. Pascal was one of the founders of probability theory, and the wager is among the earliest pieces of decision-theoretic reasoning in the philosophical literature, which is why it is discussed by people with no interest in its conclusion. And the fragment opens by conceding that reason cannot settle whether God exists. That concession is the argument's premise rather than an embarrassment: the wager is addressed precisely to someone who has worked through the material in the preceding five articles and found it inconclusive.

The passage contains three distinct arguments, which Alan Hájek separates in the standard reference treatment of it.

The first turns on dominance. Set out the options: wager for God or against, and God exists or does not. If God does not exist, the two choices come out roughly the same, and if God does exist, wagering for God is infinitely better. So one option is never worse than the other and is sometimes very much better, and choosing it requires no probability judgement at all.

The second uses expected value with an assumption that the probability is even, and concludes that the expected value of wagering for God exceeds that of the alternative.

The third generalises the second and is the version that matters. Take any probability of theism you like, however small, provided it is not zero. Multiply it by an infinite payoff. The result is infinite. So the expected value of wagering for God is infinite whatever finite probability you assign, and the argument does not need the probability to be even, or high, or anything at all except not zero.

The power of that third version is worth registering, because it is genuinely impressive. It makes the argument immune to the objection that theism is improbable. A critic who has spent five articles arguing that the evidence is weak has, on this argument, conceded everything Pascal needs, since weak evidence still leaves a non-zero probability.

The immunity is bought with the infinity, and every serious objection to the wager attacks the purchase rather than the reasoning.

The rivals

Diderot put the point in 1746: an imam could reason in exactly the same way. The structure of the wager makes no reference to any feature of Christianity, and a wager for any faith promising infinite reward has the identical form and the identical expected value.

J. L. Mackie developed this in The Miracle of Theism in 1982, running through the traditions and denominations that could each mount the argument, several of which hold that adherents of the others are precisely the people who are not saved. Since the wager gives no way to choose between them and they cannot all be taken up, it has failed to recommend anything.

The objection can be made much worse, and James Cargile showed how. Nothing requires the rival hypotheses to be actual religions. For any real number, one can posit a deity who confers infinite reward on those who contemplate that number above all else. This generates infinitely many rivals with identical structure, and shows that the objection is not a point about the accidental plurality of world religions but a structural feature of the reasoning.

Two replies are available and each has a cost that should be stated.

The first restricts the argument to hypotheses that are live options for the person considering them, which is a notion borrowed from James and set out below. Pascal was writing for people already inside a Christian culture for whom the invented deities are not real possibilities. The cost is that the argument's force now depends on the wagerer's cultural starting point, which is an odd feature for a piece of decision theory to have, and it means the wager cannot function as an argument addressed to anyone in particular about which religion to adopt.

The second reply says that perverse deities are far less probable than the traditional one. This reply fails, and it fails in a way that illuminates the whole argument. On the third version of the wager, any non-zero probability yields infinite expected value. So the perverse deity's low probability does not reduce its expected value below the traditional one; both are infinite, and infinite expectations do not compare in the way finite ones do. The feature that made the argument invulnerable to low probability also makes it unable to prefer the probable to the absurd.

The machinery breaks

Hájek pressed a further objection that is decisive in a different way, and it concerns mixed strategies.

Suppose wagering for God has infinite expected value. Now consider this policy: toss a fair coin, and wager for God if it comes up heads. There is a one-half chance of an infinite payoff, and one half of infinity is infinity, so this policy also has infinite expected value. So does a policy with a one-in-a-million chance. So, for that matter, does almost anything a person might do, since almost any action leaves some non-zero chance that the person ends up believing eventually.

The consequence is not that the wager recommends the wrong thing. It is that the wager recommends everything equally, and an argument whose output is that all available actions are tied has not given anyone a reason to do anything.

The general lesson is that standard expected-value reasoning is not built to handle infinite utilities and does not survive contact with them. This is a known problem in decision theory rather than a point invented to embarrass Pascal, and it shows up in other settings where infinite payoffs are introduced. Reformulations of the wager that avoid it have been attempted, using bounded utilities or non-standard analysis, and none has become the standard version.

Can you decide to believe?

The wager issues an instruction: believe. And belief does not appear to be the kind of state that takes instructions. Try, now, to believe that there is a horse standing behind you. Not to imagine it, or to act as though there were one, but to believe it. Nothing happens, and the failure does not feel like weakness of will.

Bernard Williams argued in "Deciding to Believe", collected in Problems of the Self in 1973, that the impossibility here is conceptual rather than merely psychological. Suppose someone could believe at will. Then they could bring themselves to hold a proposition true while knowing that they had acquired the state through a decision and not through any indication that it was true. Williams's question is whether a state acquired that way, and known by its holder to have been acquired that way, would be a belief at all, given that believing something is holding it to be true and is answerable to how things are.

Pascal saw this objection coming and answered it, and his answer is the reason the wager remains interesting rather than a curiosity.

He grants that you cannot believe by deciding to. What you can do is act. Go among believers, follow the practices, take the holy water, have the masses said. His diagnosis is that the obstacle to belief is not intellectual but a matter of the passions, and that acting as a believer acts will over time quiet the passions and the belief will follow. The wager therefore governs actions, which are voluntary, and belief arrives as a downstream effect.

Williams accepts that this indirect route exists and holds that it works only through a kind of self-deception. The person has deliberately arranged to acquire a belief by a process they know is not truth-directed, and for the arrangement to succeed they must lose sight of what they did. Whether that description is fair to religious practice is contested by people who think of the practices as a way of becoming able to see something rather than a way of installing a conviction.

The dispute matters beyond this article. Evidentialism, from the beginner tier, is a norm about how beliefs ought to be formed, and a norm presupposes that its subject has the relevant control. If belief is not voluntary in any direct sense, then evidentialism has to be restated as a norm about the practices and habits that shape belief, and once restated it becomes considerably harder to use against the believer.

James's version

James delivered "The Will to Believe" as a lecture in 1896, and it became the title essay of The Will to Believe and Other Essays in Popular Philosophy in 1897. His argument is more careful than its reputation, and its target is the position set out in the beginner tier under Clifford's name.

An option is a choice between hypotheses, and James calls it genuine when it meets three conditions. It is living when both hypotheses are real possibilities for the person facing it, which is a fact about that person rather than about the hypotheses. It is forced when there is no third way, so that declining to choose has the same practical effect as choosing one side. It is momentous when the stakes are significant and the opportunity may not come again.

The second condition does the work. Clifford's rule assumes that suspending judgement is always the safe course, because a person who believes nothing without sufficient evidence never believes anything false. James's reply is that this describes only one of two goals. We want to believe truths and we want to avoid errors, and these are different aims that recommend different policies. A policy guaranteeing you never believe a falsehood also guarantees that you miss every truth you could not prove, and describing that as the cautious option conceals that it is a choice with its own costs.

Where the option is forced, withholding is not neutral. If religion is false, the agnostic loses nothing by remaining uncommitted. If it is true, the agnostic loses whatever the committed gain, and loses it just as thoroughly as someone who positively denied it. On that construal the evidentialist rule is not a way of avoiding risk but a way of taking one particular risk without noticing.

James also pointed to a class of cases where belief is partly self-fulfilling: situations in which the outcome depends on someone's believing it will occur. Trusting a stranger who will respond to being trusted, or joining a collective effort that succeeds only if enough people expect it to. These cases are genuine, they are a real limitation on evidentialism, and James extended them considerably further than they reach.

The essay drew immediate criticism for appearing to license believing whatever one would like to be true, and James later said he should have called it the right to believe. That is a concession worth noting and it is smaller than it looks. The three conditions restrict the licence sharply, and the essay does not permit belief against the evidence, only where evidence is genuinely inconclusive.

The place critics press hardest is whether religion is a forced option. The agnostic denies it, holding that suspended judgement is a stable and honourable third position rather than a disguised negative, and that James defined that position out of existence rather than arguing against it. James does not have a strong answer to this, and it is the objection his defenders have had the most trouble with.

Next

The six articles so far have been about the case for theism, assessed on its own terms. The remaining articles in this tier turn to the case against, beginning with the objection that has done more to move people out of religious belief than every argument in this tier has done to move them in.