Pascal's Wager Is A Good Argument

Should you take the wager?

Pascal’s wager

Pascal’s wager might be the most unfairly maligned argument in all of history. It’s commonly brushed off in just a few sentences. I remember years ago watching an atheist tier-list declare Pascal’s wager F-tier, before claiming that it commits “the black and white fallacy.” Another declared Pascal’s wager defective because it, in his words, “doesn’t even attempt to argue that God exists,” which is a bit like declaring a car defective because it isn’t edible—that’s simply not what it’s designed to do.

I think Pascal’s wager is remarkably compelling. It may very well be that even if you think some religion is probably wrong, you should wager on it still.

The short version of Pascal’s wager is that getting the right religion has potentially infinite value. Heaven is an infinitely nice place, and in it you get to spend eternity with the source of limitless perfection himself. A second of heaven contains more joys than all of the naturalistic pleasures that have existed so far in history. Alexander Pruss has a nice analogy for the goodness of God:

God’s value is related to other infinities like (except with a reversal of order) zero is related other infinitesimals. Just as zero is infinitely many times smaller than any other infinitesimal (technically, zero is an infinitesimal—an infinitesimal being a quantity x such that |x| < 1/n for every natural number n), and in an important sense is radically different from them, so too the infinity of God’s value is infinitely many times greater than any other infinity, and in an important sense is radically different from them.

Hell, in contrast, sucks. Traditional views hold that it’s an eternity of misery. Think about how bad it would be to be tortured for a thousand years. Hell is infinity times worse than that. Even if hell is temporary, every moment out of heaven results in infinite lost well-being. It would be rational to endure 1,000 years of torture for an extra millisecond in heaven.

Accepting the right religion might improve your time in heaven for at least two reasons. First, spending a lifetime as part of the religion that most venerates God may deeper your connection with God, thus making heaven better. Second, various theological views hold that believing the right thing—trusting in Jesus, for instance—is required to get into heaven. Even if those who don’t believe in this life are eventually brought into heaven, it’s best not to risk it, and believing in this life can fast-track your route into heaven. If Christianity is true, for instance, it is rather clear that hell is a real place and that going there isn’t good. Even if the goats are eventually reunited with the sheep, it’s best to be a sheep from the beginning.

Let’s say your credence in Christianity is one in thirty-thousand. This seems pretty absurdly low—you should generally have a non-trivial credence in any view believed by a sizeable share of the smartest people who ever lived. Suppose that conditional on Christianity, you think the odds are 10% that believing it will increase your eternal reward. This still means that being a Christian has infinite expected value. It increases the odds of eternal reward by one in 300,000.

Presumably it would be worth performing some action if it gave you a 1/300,000 chance of infinite reward. If by working on reducing nuclear risks, you could lower the odds of the end of the world by one in 300,000, then that would seem like a valuable career, even if atheism is true. By conservative estimates, wagering on the right religion is better.

That’s the basic argument for accepting Pascal’s wager. There are a lot of responses, but I think most of the popular ones are very weak, for reasons I’ll explain. For more reading on this subject, I recommend this article and this article.

Black and white fallacy

A common response from new atheists who couldn’t tell metaphysics from Metamucil is that Pascal’s wager commits the black and white fallacy. There are more than two options: atheism and Christianity (or whichever other religion it is claimed one should wager on). Thus, merely treating it as an argument for Christianity is fallacious.

Now, this is obviously correct as far as it goes. Pascal’s wager does not automatically tell you to wager on Christianity. Rather, it tells you to wager on whichever religion you think is likeliest. Suppose, that you think there’s a 10% chance of Christianity which requires you to believe it to be spared from hell, a 1% chance of Islam which requires you to believe it to be spared from hell, and a 5% chance of Hinduism that requires you to believe it to be spared from hell.

In this case, following the wager, you should believe Christianity because doing so minimizes the risks of you going to hell and maximizes the risk of entering heaven. There might be more complicated considerations—e.g. it might be that a single moment in Christian heaven is better than eternity in Muslim heaven—but barring that, you should just go with whichever one is most probable. You should take actions which make it likelier that you’ll spend forever in paradise.

The core logic of the wager doesn’t change just because there are more options. You should still pick the one with the best prospects.

You can’t choose what to believe

Another common response to Pascal’s wager is to say “you can’t choose what to believe.” Thus, it doesn’t even make sense to wager on religion because you can’t choose to believe a religion. I think this is pretty clearly wrong:

1. The kind of attitude that the religions want you to have isn’t quite belief. It’s something more like commitment—acting like the religion is true, hoping that it is true even if you’re not totally certain that it is, and promoting it. Jesus helps a man who requests his help but says “I believe; help my unbelief.” Clearly this man doesn’t have extreme confidence that Jesus is God, but he still has the requisite kind of attitude for religious faith—trust. Christians will be in almost universal agreement that a person who gives his life for Christ despite thinking Christianity has only a 30% chance of being true has faith of the right kind.

2. Even though you can’t choose to believe, you can do things that make it a lot more likely that you’ll believe. For example, you can read the smartest advocates of some religion. You can pray and ask God to help you believe. You can attend religious services and make friends of the same religion. You can talk to my friend [redacted] who has about a 30% chance of convincing you that Christianity is correct.

3. Even if you never manage to convince yourself, you can convince other people of a religion. Once you’re convinced of the basic logic of Pascal’s wager, this is a deeply beneficent act—it provides infinite expected benefit for others! So this is a reason to live the lifestyle of the religion that you have the highest credence in, even if you’re not ultimately convinced that it’s true. It’s a reason to raise your children religious and try to convince others to adopt the religion.

Isn’t this self-serving?

Another response: isn’t Pascal’s wager self-serving? You’re picking a religion so that you can get infinite reward and be spared from infinite punishment. Isn’t this kind of selfish? However:

1. It isn’t actually wrong to do things for self-interested reasons unless those things harm others. For example, no one thinks that you act wrongly by abstaining from eating poison, on grounds that doing so is selfish. But picking a religion doesn’t harm others, so it’s alright to do it for self-interested reasons. It’s not wrong to do things that spare yourself from infinite expected suffering.

2. Going to heaven isn’t just good for you—it’s good overall! It is better to spend time in communion with the source of all goodness than working against him. If Christianity is true, for instance, serving Christ is morally righteous.

3. By being religious, you increase the odds that the people around you will be religious. This means that your action produces infinite benefits for other people, making it the exact opposite of being self-centered. In fact, I think there is something particularly noble about performing an action based on it having good expected consequences, even if you don’t find it emotionally enticing. Abstract pursuit of the good, even when it doesn’t resonate with you emotionally, is noble.

What if you’re making the real God madder and madder?

Leading scholar on Pascal’s wager Homer Simpson argues “Suppose we’ve chosen the wrong god. Every time we go to church we’re just making him madder and madder!”

Now, I can imagine a person buying this objection if they’re totally in the dark about which God/gods are most likely to run the world and think it’s decently likely that jealous and vengeful gods who hate people of the wrong religion run the world. But I don’t think you should buy this:

1. The idea that there is a roving band of Zeus-like characters is very implausible. Surely some of their actions would be notable enough for us to have heard about them. But if there is an all powerful, all good being, he wouldn’t be jealous and get mad. If anything, he’d be likely to reward those who sincerely seek religions, make sacrifices for the sake of what they believe to be following him, and try to seek him.

2. Even if God gets marginally disappointed, this is very likely outweighed by the increased probability of entering heaven. Christians, Muslims, and Jews agree that a randomly selected theist is in better shape than a randomly selected atheist. Christians will even generally think that a Muslim who attempts to serve God is in better shape than an atheist! And, of course, if you get the right religion, then this has very good prospects—both for you and others! Thus, if anything, this response backfires; your prospects are likely better from wagering on the wrong religion than no religion at all.

3. At the very least it seems one convinced of this position should try to serve God even if they’re unsure as to his nature. Maybe they shouldn’t wager on a specific religion, but they should pray sincerely an attempt to live a life devoted to God.

4. If there is a true religion, it’s very unlikely that the religion would have a tiny number of adherents. If God is going to enact his will on Earth, he’d do so in a major way. So then the only religions one must choose between are the major religions—Christianity, Islam, Hinduism, and so on. I think Islam is pretty implausible, so the odds of you picking the right religion, conditional on there being one, are non-negligible.

Discount low risks?

Another reply to Pascal’s wager: perhaps we should discount risks that are very low! If a risk is, say, below one in a billion, maybe we should just ignore it, no matter what the consequences are. In addition, it might be that utility is bounded, so that as the amount of time spend in heaven approaches infinity, the goodness of that approaches a finite integer. However:

1. Even if you discount low risks, it’s not clear why the risk is so low that religious commitment has infinite utility. As I explained at the start of the article, even if infernalism is false—even if all are saved—it still is plausible that our actions have infinite expected utility by speeding up our entry into heaven and strengthening our relationship with God. Surely one’s credence in this shouldn’t be less than one in a billion. If the risks are one in 300,000—well, a 1/300,000 chance of an infinitely good outcome is clearly worth taking. 300,000 is not anywhere near the point at which it’s permissible to discount.

2. You shouldn’t have a credence of zero in eternal hell. There are lots of very smart Christians and Muslims who believe in an eternal hell. If lots of people smarter than you believe some proposition, you should rarely think the odds of the proposition are very near zero. But if you take this into account, then it makes sense to wager.

3. I don’t think discounting low risks or accepting bounded utility makes any sense. I’ve made this case at great length here, so I’d encourage you to read that if you want to hear more. But one brief argument is that if you’re offered 100 years in paradise, surely that is less good than a 99.999% chance of 100,000 years in paradise, which is less good than a 99.99% chance of 10,000 years in paradise. So long as lowering the odds of payment by .000000000000001% while increasing the quantity of payouts by a factor of a trillion always makes the deal better, then there’s no risk threshold beneath which you discount risks. In addition, if you discount low risks, for complicated reasons explained in the post, you’ll need to think that whether you should take an action will sometimes depend on causally-unrelated things happening galaxies away, which is pretty insane.

You are biased

I think we’re mostly pretty biased against Pascal’s wager. When I consider the argument, I notice in myself an extreme psychological aversion to it—a desire to disprove it. This is because:

1. Humans instinctively round low risks down to zero. Whether a risk is 1/100,000,000 or one in a billion, we simply register it as functionally equivalent to zero.

2. We don’t have reliable intuitions about big numbers. People will pay the same amount to save 2,000 birds as 20,000 birds or 200,000 birds. Even though eternity is infinitely longer than a mere 10 quadrillion years, they register as the same in our minds. Thus, it’s not remotely surprising that we’re biased against Pascal’s wager, where the wager is something our intuitions demonstrably underestimate.

3. We’re particularly biased by partisanship. Humans are motivated to believe whatever facts are most convenient to their own side. Thus, when an argument comes along for why we should wager on a belief that we think is probably wrong, it’s no surprise we’re biased against it. It’s for the same reason that political partisans would be biased against arguments for why the candidate that they don’t like raises the odds of infinite utility being brought about.

For these reasons, I think we often apply way too much scrutiny to Pascal’s wager and are willing to accept bad arguments against the wager. Beware! I think people would be a lot more sympathetic to Pascal’s wager if they could more firmly grasp how good heaven is—if they really, intuitively could grok that the experience they’re gambling for infinitely surpasses all joys they’ve experienced before, both quantitatively and qualitatively. That a single moment of heaven is worth a trillion years of excruciating torture.

Conclusion

There’s obviously a lot more to be said about the wager. As a personal note, I haven’t taken it though I think a lot of that has to do with my own psychological defects. But hopefully, I’ve explained why most of the common responses that people give don’t work. You shouldn’t just shrug off the wager—it merits serious thought, whatever you end up ultimately concluding about it. And you probably shouldn’t wager on atheism!