2 Why You Should Bet on God
2.1 Introduction
I am going to try to convince you that you should believe in God. But I’m going to do it in a different way than you might expect. I’m not going to give you an argument that God exists. I won’t try to convince you, for instance, that there has to be a God in order to serve as a first cause of the universe (what’s sometimes called “the cosmological argument”), or that we have to posit an intelligent designer in order to explain all the forms of life and other complex systems we find in the world (what’s sometimes called “the design argument”). Rather, I’m going to argue that you should believe in God because it’s in your best interest to do so.
Here’s an analogy, to give you a feel for the sort of argument I’m going to give. Imagine that you’re at a casino and you’re deciding whether to bet your $10 on red or on black at the roulette table. But it’s not a regular game of roulette. The way it works is that if you bet on red and win you walk away with $20, and if you bet on black and win you walk away with a million dollars. You don’t know whether it will land on red or black. And yet you know exactly what to do: bet on black. Why? Because you stand to gain so much if it comes up black and stand to lose so little if it doesn’t. Similarly, you have no way of knowing whether or not God exists. Still, you should believe in God. Why? Because you stand to gain so much by believing in God and stand to lose so little. Indeed, only by betting on God do you stand a chance of winning the ultimate jackpot: eternal afterlife in heaven.
In Sections 2.2–2.3, I’ll give a more careful and rigorous presentation of this argument. Then, in Section 2.4, I’ll address some potential objections to the argument, for instance that it’s extremely unlikely that God exists or that belief alone is not enough to guarantee entrance into heaven. Finally, in Section 2.5, I address the worry that it’s impossible to make yourself believe in God through sheer force of will, no matter how convincing you find the argument.
2.2 Practical Reasoning in an Uncertain World
In this section, I will take a big step back from the question of whether you should believe in God, and look more generally at how we make rational decisions about what to do in situations of uncertainty. After looking informally at the sorts of factors we take into account when making such decisions (2.2.1, I lay out a more rigorous way of thinking about rational decision-making, in terms of “expected utility calculations” (-sec-expected-utility-calculations).
2.2.1 Costs, Benefits, and Likelihoods
Let’s shift from the roulette-wheel example to something more realistic. You’re at a party and you spot your crush across the room. You’re trying to decide whether to go talk to him (or her, but let’s go with “him”) and confess your feelings. The night is young and you’ve still got your wits about you, and you want to make a smart decision. What sorts of things do you need to take into account?
First, you need to think about your options and the possible outcomes. Your options are telling him that you’re crushing on him or saying nothing. (What about flirting without blurting? We’ll get to that; let’s keep it simple for now.) And the possible outcomes are that he likes you back or that he’s not into you.
Second, you need to consider the costs or benefits of each eventuality, that is, each way things might unfold. If you confess your feelings to him and he’s into you too, you get to date your crush and you’ve won big. If you confess your feelings and he’s not into you, you’ll probably have some mix of embarrassment that he turned you down but maybe also pride that you had the courage to take a risk. If you don’t confess your feelings but actually he is into you, you’ve missed a huge opportunity. And finally, if you don’t confess your feelings and he isn’t into you, you’ve dodged a bullet.
Third, you need to think about how good or bad the different costs and benefits are, relatively speaking. What’s worse: the embarrassment of getting turned down or missing out on the opportunity? Probably the missed opportunity is worse. Then again, if you’ve got a new crush every weekend, you’re incredibly sensitive about being rejected, and you have plenty of other interested suitors, maybe the embarrassment is worse. It’s going to vary from person to person, and what you ought to do will depend in part on how good or bad the different eventualities are for you.
Finally, you need to take into account the likelihood of each of the possible outcomes. Obviously, it makes a difference whether the chances that he likes you back are very good or very slim. If there’s virtually no chance that he’s into you, then it’s not worth the risk of embarrassment. If it’s more or less certain he is into you—if he’s been sending you heart emojis all day and keeps winking at you from across the room—then it’s not worth worrying about the insignificant chance of embarrassment.
Somehow or other, you weigh all these different factors and make a smart decision about what to do. In fact, you do this sort of thing all the time: deciding whether to lug around an umbrella all day when you’re not entirely sure if it’s actually going to rain; deciding whether to turn back when you remember you forgot to lock the front door and you’re already five minutes away; deciding whether to go see a certain movie when you’re not sure if it’s going to be any good; and so on. And you do it without the help of a calculator and without having to write out a pro/con list. But there is a more rigorous way of thinking about such decisions, and it will prove to be a useful tool for thinking about them—and, in particular, for thinking about whether to believe in God.
2.2.2 Expected Utility Calculations
We can model the decision about talking to your crush by using a certain sort of “decision matrix.” The matrix will represent the options available to you (as rows), the possible outcomes (as columns), and the likelihood of each outcome. And it will use numerical values to represent your rankings of the different eventualities (that is, option/outcome pairs).
To make this a bit more concrete, let’s suppose that in the crush case the eventualities are ranked from best to worst as follows (where a higher number represents a better eventuality):
- 4. Confess your feelings and he’s into you
- 3. Don’t confess your feelings and he’s not into you
- 2. Confess your feelings and he’s not into you
- 1. Don’t confess your feelings and he is into you
And let’s suppose you think there’s about a 75% chance that he likes you back. Then the matrix would look like this:
| He’s into you 75% |
He’s not into you 25% |
Expected Utility | |
|---|---|---|---|
| Confess your feelings | 4 | 2 | 3.5 |
| Don’t confess your feelings | 1 | 3 | 1.5 |
I’ve snuck in an extra column for expected utility. This is the column we’ll use to crunch the numbers, calculating what the smart choice is for you, given your preferences and the likelihoods of the different outcomes. Before I explain where these numbers (3.5 and 1.5) are coming from, let me say something about how to think about these expected utilities.
In effect, the expected utility of an option tells you how well you’d do, on average, if you kept choosing that option over and over again. Imagine that you’re in an infinite loop. You choose an option, and then time rewinds and you choose that same option again and again—and 75% of the time he’s into you and 25% of the time he isn’t. The fact that confessing has an expected utility of 3.5 and not confessing has an expected utility of 1.5 tells you that on average you’d do a little over twice as well by repeatedly choosing to confess your feelings than by repeatedly choosing not to (since 3.5 is a little over twice as much as 1.5). And what that tells you is that the smart thing to do is to confess your feelings.
But where exactly are these numbers coming from? To calculate the expected utility of a given option, you multiply the value of each possible outcome of the action by the likelihood of that outcome, and add together the results.
- Expected Utility
- The expected utility of an action is a measure of how well you should expect to do if you choose a given option. Multiply the value of each outcome by its likelihood, and take the sum of those products.
Put in terms of the rows and columns of Matrix 2.1: to calculate the expected utility of the top row, you multiply the value in the top row of the first column by the likelihood associated with that column, multiply the value in the top row of the second column by the likelihood associated with that column, and add the results together. So, we get:
\[ \begin{align} \textsf{Confess your feelings} &= (.75 \times 4) + (.25 \times 2) = 3.5 \\ \textsf{Don't confess your feelings} &= (.75 \times 1) + (.25 \times 3) = 1.5 \end{align} \]
The specific numbers themselves don’t have much significance. It’s not as if you get 3.5 “units” of happiness by confessing your feelings, or anything like that. What matters is the relative differences between the expected utilities for different actions: the expected utility of telling your crush how you feel (3.5) is over two times as big as the expected utility of not telling him (1.5).
This gives us an argument for confessing your feelings:
Premise CF1 is justified by the fact that, in ordinary cases like this, these decision matrices and expected utility calculations do such a good job of reflecting the rational thing to do in situations with uncertain outcomes. And premise CF2 is reasonable to the extent that we have filled in the matrix correctly, ranking the eventualities and assigning probabilities to the outcomes in a sensible way.
There are two more things I want to point out about this model of decision-making before I (finally) bring us back around to the question of believing in God. First, by using 1 for the worst eventuality and 2 for the second-worst, that means that the worst-case scenario is only twice as bad as the second-worst. But sometimes the worst-case scenario is way worse than any other eventuality. Suppose for instance that you do very badly with humiliation, and that for you a rejection is about 100 times worse than a missed opportunity. We can represent that by using a weighted ranking, giving the eventuality of confessing and getting rejected a value that’s 100 times lower than the others:
| He’s into you 75% |
He’s not into you 25% |
Expected Utility | |
|---|---|---|---|
| Confess your feelings | 100 | 1 | 75.25 |
| Don’t confess your feelings | 98 | 99 | 98.25 |
Now, the expected utility of confessing is less than the expected utility of not confessing, and so the calculations tell us that you ought to hold your tongue—which is the right result if you really do take rejection that hard.
Second, I’ve obviously oversimplified the example by pretending that there are only two possible outcomes. Really, there are at least three different ways things could turn out: he’s into you, he’s not into you and he rejects you in front of everyone, or he’s not into you but he discreetly and privately rejects you. We can get more fine-grained about your options too: confess your feelings, flirt a little, or completely avoid him. Our model for decision-making can easily accommodate this simply by adding extra rows and columns to our decision matrix:
| He’s into you ___% |
He privately rejects you ___% |
He publicly rejects you ___% |
Expected Utility | |
|---|---|---|---|---|
| Confess your feelings | ___ | ___ | ___ |
___ |
| Flirt with him | ___ | ___ | ___ _ | __ |
| Avoid him | ___ | ___ | ___ _ | __ |
All you have to do is figure out a weighted ranking of the different eventualities, estimate the likelihood of each of the different outcomes, crunch the numbers, see which option has the greatest expected utility, and—voilà!—now you know what you should do.
2.3 The Expected Utility of Believing in God
This same sort of reasoning from expected utilities can be put to work in an argument that you ought to believe in God:
Premise BG1—which is exactly the same as CF1 above—is justified by the fact that it is so sensible to rely on expected utility calculations in the sorts of ordinary examples considered above. If you thought the option with the greatest expected utility is the smart choice in all other cases, it would be weird and unprincipled to think it isn’t the smart choice in just this one case of deciding whether to believe in God.
To justify BG2, we have to construct the decision matrix. And that’s going to look something like this:
| God exists 50% |
God doesn’t exist 50% |
Expected Utility |
|
|---|---|---|---|
| Believe in God | \(\infty\) | 2 | \(\infty\) |
| Don’t believe in God | 1 | 3 | 2 |
Since we don’t know one way or the other whether God exists, I’ve assigned a probability of 50% to God existing and 50% to God not existing. I’ve given the lowest score (1) to the eventuality of not believing he exists when he in fact does, since that presumably means you’re going to hell. The second lowest (2) goes to the eventuality in which you do believe in God but he doesn’t exist, since in that case you’ve been wasting your time going to church, praying, and living an upstanding religious life. Slightly better (3) is being an atheist and being right about it, since then you get all the benefits of an atheist lifestyle (for instance skipping church) without any punishment at the end. Top score goes to the eventuality in which you believe in God and God does turn out to exist, and this gets a value of infinity (\(\infty\)) rather than 4, since the amount of pleasure and fulfillment you receive in an eternal afterlife in heaven is infinitely greater than what you get in any of the other eventualities.
We then calculate the expected utilities in just the way we did in Section 2.2.2. The calculation in the second row is straightforward arithmetic:
\[ \begin{align} (0.5 \times 1) &+ (0.5 \times 3) \\ 0.5 &+ 1.5 \\ &\ 2 \end{align} \]
So the expected utility for not believing in God is 2. As for the first row, the expected utility of believing in God, is:
\[(0.5 \times \infty) + (0.5 \times 2)\]
But what’s \((0.5 \times \infty)\)? In other words, how many things do you have left if you take infinitely many things and then remove half of them? Answer: \(\infty\). (Take all the numbers and remove all the odd ones. You’re still left with infinitely many even numbers.) So, when we do the math,
\[ \begin{align} (0.5 \times \infty) &+ (0.5 \times 2) \\ \infty &+ 1 \\ &\infty \end{align} \]
So the expected utility of believing in God is \(\infty\).
Finally, we need to compare the expected utilities of the two options. Which is greater: \(\infty\) or 2? Obviously \(\infty\). So, the expected utility of believing in God is greater than the expected utility of not believing in God. And that’s the argument for BG2.
2.4 Challenging the Decision Matrix
The argument for BG2 relies on a number of assumptions I made about how to fill in the decision matrix (Matrix 2.4): the range of possible options and outcomes, the likelihood of the different outcomes, and the relative goodness or badness of the different eventualities. Thus, one way of challenging BG2 is to insist that, in one way or another, I’ve constructed or filled in the decision matrix incorrectly. In this section, we’ll consider a variety of different challenges of this kind.
But before turning to that, let me quickly dispense with a different line of objection, which some readers may find tempting. People sometimes object that the argument rests on some sort of conceptual error simply because it invokes the notion of infinity. They say that it doesn’t make any sense to talk about infinity, or to compare infinite quantities with finite quantities, or something to that effect. But surely that’s not right. Suppose you’re choosing between two offers for free movie tickets. One gives you free entry to twenty movies. The other gives you limitless free entry: no matter how many times you go for free, you can always go for free again. Do you throw your hands up and say “How could I possibly decide?? It makes no sense to talk about limitless tickets!” No, you accept the second offer. And it makes perfect sense why you would: because the second offer, despite involving an infinite quantity, gives you more of a good thing than the first.
2.4.1 Wrong Probabilities
One might complain that I’ve grossly overestimated the probability that God exists, by assuming that it’s a 50/50 chance that he exists. Perhaps you think it’s extremely unlikely that God exists. Surely, though, you’ll admit that it’s at least possible that God exists. If you die and are ushered into God’s presence, you’ll be surprised, but not in the way that you’d be surprised if you were ushered into the presence of something you think is genuinely impossible, like a round square.
So, let’s say it’s a 1% chance that God exists (though the response I’m about to give will work even if you think it’s a .00000001% chance). In that case, we need to update a couple of the boxes in the original decision matrix:
| God exists 1% |
God doesn’t exist 99% |
Expected Utility |
|
|---|---|---|---|
| Believe in God | \(\infty\) | 2 | \(\infty\) |
| Don’t believe in God | 1 | 3 | 2.98 |
Changing the probabilities required us to recalculate the expected utility of not believing in God. It shot up almost a whole point! But the expected utility of believing in God doesn’t change at all. Why is that? Let’s crunch the numbers. What’s .01 x \(\infty\)? In other words, what do you get when you have infinitely many things, and you take away 99 out of every 100 of them? Answer: \(\infty\). Now add 1.98 (= .99 x 2) to that, and you get \(\infty\). The expected utility of believing in God doesn’t change and is still greater than the expected utility of not believing in God. Thus, so long as there is some chance that God exists, however small it may be, the argument for BG2 still works.
2.4.2 Belief Isn’t Enough
You might object that believing in God isn’t all by itself enough to get into heaven. You might think that you also have to meet some further conditions, for instance that you led a good, moral life and followed God’s commandments. I might ask you how you know that, but then again you might ask me how I know that badly-behaved believers go to heaven. (Touché.) So, let me just grant the point for the sake of argument: only well-behaved believers get into heaven. What that means is that the original decision matrix is inadequate, since it runs together two importantly different options: being a well-behaved believer and being a badly-behaved believer.
The fix is to expand our matrix so that each of these options has a row of its own.
| God exists 50% |
God doesn’t exist 50% |
Expected Utility |
|
|---|---|---|---|
| Believe in God and be good |
\(\infty\) | 3 | \(\infty\) |
| Believe in God and be bad |
2 | 4 | 3 |
| Don’t believe in God |
1 | 5 | 3 |
The new row introduces new eventualities, which means we have to redo the rankings. I gave a 1 to the eventuality in which you don’t believe in God and yet he does exist, and a 2 to being a badly-behaved believer, on the assumption that God will punish you for that too but will be a little more lenient since you at least believed in him. I’ve scored being an atheist in a Godless world (5) higher than being a badly-behaved believer in a Godless world (4), and I’ve ranked both ahead of the life of a well-behaved believer in a Godless world (3). Finally, the eventuality in which you’re a well-behaved believer and God does exist gets \(\infty\), since this is what will get you into heaven, and that’s infinitely better than any of the other eventualities.
So, what does this all mean? What it means is that—assuming that you have to be a well-behaved believer to get into heaven—being a well-behaved believer has greater expected utility than either being a badly-behaved believer or not believing in God at all. It’s still true, then, that the option with the greatest expected utility requires you to believe in God. So, we have not yet found a reason to reject BG2.
It may be that I haven’t gotten all the scores exactly right. Maybe I’m wrong, and God gives exactly the same punishment to both nonbelievers and badly-behaved believers. In that case, you could make it a tie and change the 2 in the first column to a 1. Or maybe I’m wrong that the life of an atheist in a Godless world is more rewarding than the life of a believer in a Godless world. Fine, we can lower the score for “God does not exist” in the bottom row. It doesn’t matter. The argument still goes through, since the expected utility of being a nonbeliever or a badly-behaved believer still comes out to be some finite number, whereas the expected utility of being a well-behaved believer will be infinite.
2.4.3 Heaven May Be Finite
The reasoning behind BG2 takes for granted that God rewards believers with something that’s infinitely valuable, for instance an eternal afterlife filled with an infinite amount of pleasure. But I haven’t offered any evidence or argument for that. For all we know, God rewards believers only with some finite amount of pleasure—maybe ten years in heaven. And one might object that this imperils the argument: if we can’t be sure that believers stand to receive something of infinite value, then there’s no guarantee that the expected utility of believing will be infinite, and thus no guarantee that it will come out greater than the expected utility of disbelief.
But that’s the wrong way to look at it. Let’s just acknowledge that we can’t be sure whether God is generous and rewards believers with something of infinite value or whether God is stingy and rewards believers with something of finite value. That means that Matrix 2.4 is oversimplified, and that we need to expand the decision matrix to include three columns: one for the possibility of a generous God who offers infinite rewards, one for the possibility of a stingy God who offers only finite rewards, and one for the possibility that there’s no God.
| Generous God exists 25% |
Stingy God exists 25% |
No God exists 50% |
Expected Utility |
|
|---|---|---|---|---|
| Believe in God | \(\infty\) | 1,000,000 | 2 | \(\infty\) |
| Don’t believe | 1 | 1 | 3 | 2 |
I’ve valued the eventuality in which you’re a believer and God turns out to be stingy at 1,000,000 to reflect the idea that it’s still many orders of magnitude better than the next best eventuality, in which you’re a nonbeliever and God doesn’t exist. Again, though, the exact values don’t really matter, nor do the exact probabilities. All that matters is the \(\infty\) on the top left, since that’s going to ensure an infinite expected utility for believing in God. So, even if we can’t be sure that God rewards anyone with an infinitely valuable afterlife, we still get the result that we ought to believe in God.
2.4.4 Many Gods to Choose From
Let’s consider one last objection to BG2. You might worry that getting into heaven isn’t simply a matter of believing in God. You’ve got to believe in the right God. If the true God is the Christian God and you believe in Zeus (or vice versa), you’re going to hell. And the decision matrix can’t tell you which God is the right God to believe in.
I think that’s right. But it’s no objection to BG2. Once again, what this shows us is that Matrix 2.4 was oversimplified. We need additional rows reflecting the different gods we can choose to believe in, and additional columns reflecting the different gods that might turn out to exist. So, let’s rectify that: *
| Christian God exists 25% |
Zeus exists 25% |
No God exists 50% |
Expected Utility |
|
|---|---|---|---|---|
| Believe in Christian God | \(\infty\) | 1 | \(\infty\) | |
| Believe in Zeus | 1 | \(\infty\) | 3 | \(\infty\) |
| Don’t believe | 2 | 2 | 4 | 3 |
Once again, I’ve done my best to assign probabilities and score the noninfinite eventualities, and once again it doesn’t much matter whether I’ve gotten the rankings of the non-infinite eventualities exactly right. And we can, if you like, expand the matrix to include more and more possible gods, but that shouldn’t affect the argument either.
What we get now is a tie for greatest expected utility. This means that the objection under consideration is right as far as it goes: we aren’t told whether to believe in the Christian God or whether to believe in Zeus. But notice that believing in some God or other continues to have greater expected utility than not believing at all. So, the decision matrix still tells us that the greatest expected utility is attained by (and only by) believing that there is a God. So, there is no successful challenge to BG2 here.
2.5 Is Belief Voluntary?
I have examined a number of ways one might challenge my decision matrix, and in each case we’ve seen that the matrix can be modified without jeopardizing the Argument for Betting on God. I can’t claim to have surveyed every possible way of challenging the matrix, but we must stop somewhere, and I think that our success in handling the objections discussed above gives us reason to be optimistic that the argument can withstand further challenges to the matrix. But let us move on to an importantly different style of objection.
Suppose you find my reasoning entirely convincing. You decide that despite all of your many reasons for doubting that God exists—it’s time to start believing in God. You say to yourself: okay, believe!! Nothing changes, you still don’t believe in God. You clench your fists, furrow your brow, and try again: believe!!! Nothing changes. You still don’t believe in God.
What you’ve just discovered is that belief is not voluntary. You don’t get to decide what to believe in the way that you get to decide what to imagine or what to say. And that’s potentially a problem for the argument, for two reasons. First, it threatens to make the argument ineffective: if the point of the argument is to get you to believe in God, then it can’t get the job done. Second, it threatens to undermine BG1. BG1 says you should always go with the option that has the greatest expected utility. But saying that you should do something implies that you can do it. Accordingly, if you can’t choose the option with the greatest expected utility—in this case, believing in God—then it’s not true that you should choose it, in which case BG1 is false.
The problem with this objection is that furrowing your brow and trying really hard to believe something different isn’t the only possible way of changing your beliefs. By way of comparison, alcoholics can’t change whether they have intense cravings for alcohol merely by willing themselves to stop craving it. But what they can do is check themselves into rehab, steer clear of their old haunts and friends who may rekindle their drinking habit, join an AA program, and so on.
Similarly, changing your beliefs isn’t something you can do directly, on the spot, by merely willing it to be so. But if you want to change your mind about God, you can do so indirectly. Go to church, read some scripture and other religious literature, surround yourself with the smartest and most inspirational believers you can find, steer clear of clever atheists, and so on. It does sometimes happen that nonbelievers find the Lord. Figure out how they did it, and follow their lead. Changing what you believe may be difficult, but that doesn’t mean it can’t be done.
We can now revise the original Argument for Betting on God to reflect the fact that changing your beliefs takes some effort.
We have already seen the argument for TB1 (a.k.a. BG1), and I’ll leave it as an exercise for the reader to construct the decision matrix for TB2. Suffice it to say that making that effort puts you in the running for an afterlife of infinite happiness, and it is the only way to be in the running for an afterlife of infinite happiness. So, even though you cannot be entirely sure in advance whether your efforts to believe will succeed, the expected utility calculations are bound to deliver the result that making the effort has infinite expected utility and that not making the effort merely has a finite expected utility.
2.6 Conclusion
I have argued that, faced with a decision between believing in God and not believing in God, the smart choice—the one with the greatest expected utility—is to believe. I defended the idea that one should prefer the option with the greatest utility by showing that it yields the right result in everyday cases (like whether to confess your feelings to your crush). I then showed how the possibility of attaining something of infinite value ensures that belief in God has the greatest expected utility. And we saw that the argument is resilient: it still works even if we suppose it’s very unlikely that God exists, even if we grant that God only rewards well-behaved believers or may only reward believers with a finitely valuable afterlife, and even once we acknowledge that entry into heaven requires betting on the right God.
Reflection Questions
- For all we know, disbelief in God or belief in the wrong God will result in being sent to hell and enduring something infinitely bad. How might the introduction of negative infinite values into the decision matrices affect the Argument for Betting on God?
- For all we know, God rewards only those who believe in him for wholesome reasons, and won’t reward those who believe in him purely out of a self-interested desire to get into heaven. Can this be used to underwrite an effective argument against BG2?
- For all we know, there is no God but rather an evil deity who punishes believers and rewards atheists. Can this observation be used to challenge BG2?
- In Section 2.4.4, we considered the objection that there are many Gods to choose from. Can that objection be strengthened by arguing that there are infinitely many Gods to choose from?
- Suppose that you are given the opportunity to enter a lottery to win an unlimited amount of money. The thing is, there’s only a one-in-a-million chance of winning, and the cost of a lottery ticket is every last dollar you have in your bank account and all of your worldly possessions. Would it be rational to enter the lottery? If not, is that a problem for BG1?
Sources and Resources
The “Argument for Betting on God” is also known as “Pascal’s Wager”. The most influential source for the argument is, as the name suggests, the 17th century French philosopher and mathematician, Blaise Pascal (Pascal 1995, fragment 680). The 11th century Persian philosopher al-Ghazālī offers a similar pragmatic argument for believing in God:
If a person calculates how long his life in this world is, and what a small fraction it is of the endless eternity which has no beginning with respect to the beginningless eternity which has no end, he knows that taking a little trouble is insignificant when set beside such great peril. He says to himself: “If they are speaking the truth, and 1 endure in such torment, what is the profit of the ease of this world, the days of which are passing few? And it is possible that they speak the truth!” (al-Ghazālī 2005, 91–93)
Asín Palacios (1920) argues that Pascal got the argument from al-Ghazālī, while Alam (2017) suggests that this sort of pragmatic argument was a common trope in Islamic apologetics, and can be found in the Qur’an itself.
The History of Philosophy without any Gaps podcast has two episodes on Pascal’s Wager:
Liz Jackson (2021) also wrote the 1000-Word Philosophy article on the topic. For something more in-depth, see Rota (2017) (Philosophy Compass). There is also this video by Rinard (2017) (Wireless Philosophy):
Much of the contemporary literature on the argument focuses on the “Many Gods” objection mentioned above, along with a “Mixed Strategies” objection not mentioned in the text. For a sharp presentation of the “Mixed Strategies” objection, see Hájek (2015). For a response to the “Many Gods” objection, see Lycan and Schlesinger (1989). For a response to both, suggesting alternative ways to measure expected utility when infinity is involved, see Jackson and Rogers (2019).
Rota (2016) offers an extended defense of “committing oneself to God,” framed around Pascal’s Wager. Garber (2009) explores the nature of the kind of “belief” that is generated indirectly, by habit rather than reason. Buchak (2018) argues that the sort of faith involved in the wager is not “belief without evidence”, but a commitment to act, developing an analogy between having faith in your partner and having faith in God.
Bostrom (2009) offers a short and punchy dialogue, suggesting that anyone who accepts such reasoning should be prepared to hand over their wallet to a mugger, if that mugger offers a high enough future reward, no matter how unlikely it is that the mugger will actually deliver that reward.
A closely related puzzle, introduced by Nicolaus Bernoulli in 1713, is known as the “St. Petersburg Paradox” (Peterson 2023). For a fun variation on this puzzle that also involves the infinite reward of heaven, see Arntzenius et al. (2004).
Donaldson (2013) (Wireless Philosophy) has more to say about the idea that you cannot simply decide to believe something in the absence of evidence: