Alan Saunders: So, there you are, in a casino, and you're at the roulette table, betting on the number five. What are the odds? There are 37 pockets in the wheel, so you draw a line on a piece of paper, and write the number 37 under it. This is the number of equally possible outcomes. You're interested in only one outcome; the number five. So you write a one above the line. And there are your odds, 1/37. This is what's called the classical theory of probability, devised in the 17th century by Pierre de Fermat, famous for his last theorem, and Blaise Pascal. The idea of probability arose in the context of gambling, of games of chance. But Pascal, a scientist, a philosopher and a devout Catholic, as well as a mathematician, was interested in odds rather simpler than those you might encounter at the roulette wheel. We're tossing a coin. Heads or tails, or to put it another way, God or no God.

Pascal's famous wager was a major contribution to decision theory and to thinking about probability. And to tell us what we've got to lose or to win and why we should make a bet, we're joined now by James Franklin, professor in the School of Mathematics and Statistics at the University of New South Wales. Jim, welcome back to the show.

James Franklin: Hi.

Alan Saunders: Now, what I've been talking about is what's known as Pascal's wager. But before we get onto that, tell us who Blaise Pascal was.

James Franklin: He was a very wide-ranging thinker from the French mid 17th century, think The Three Musketeers by way of background. Early Louis XIV. He did great work in science in his earlier days, including work on pressure, hectopascals that we measure pressure in weather, called after him. And he founded the mathematical probability theory.

Late in life, when he became very sick, he took to religion, a rather extreme form of Catholicism, and he wrote and failed to complete a book called Pensées which is a different take on the philosophy of religion. And it's that book that includes his famous wager.

Alan Saunders: So, pensées of course means thoughts, and religiously he was what was called a Jansenist, wasn't he?

James Franklin: Yes, that's right. That's a sub-sect you might say, of Catholicism, which takes an almost Calvinist view of predestination and restricts human free will, in contrast to thinking that God has done everything, including being largely responsible for your actions.

Alan Saunders: So, what is Pascal's wager?

James Franklin: Pascal says, 'Look, you've got to bet whether God exists or not, because it makes a big difference to how you live your life.' So he says, 'Think of it as like throwing a coin. Heads God exists; tails God doesn't exist. Now, if you wager that God does exist, and he does, then you will have lived the right life and God will reward you with an infinite payoff, life everlasting.

But if you wager that God doesn't exist, then it's true that you might have a more pleasant life; you have a finite amount of good fun, that you mightn't have if you lead a religious life, what with all that praying, fasting and restraining your urges. But if it turns out that God doesn't exist, well, you will be ahead. But if it turns out that he does exist and you've bet against him, then you will have lost an infinite payoff.

So Pascal says that your decision should go with the infinite payoff, even if it's hard to say whether God does or doesn't exist. The bet, the right bet, is to bet that God exists, and believe in him.

Alan Saunders: There've been many arguments for God's existence, some of them advanced in Pascal's lifetime by Rene Descartes, but this isn't one of them, is it?

James Franklin: No, it's not strictly an argument for the existence of God or even for belief. It's an argument for your accepting God, and Pascal says the conclusion of it is that you should go to mass and pray for faith.

Alan Saunders: When the Abbéde Villars published a criticism of Pascal's argument in 1671, he said, 'I lose patience listening to you treating the highest of all matters, and resting the most important truth in the world, the source of all truths, on an idea so base and so puerile, on a comparison with a game of heads and tails, more productive of mirth than persuasion.' Now, he wasn't the only person who said that sort of thing. The idea seems to be that there's something disgusting in bringing gambling into a religious argument.

James Franklin: Yes, and in fact most religious people are even more keen to say that than atheist people. They, most religious people have not liked the wager and have headed for the hills at the mere suggestion that there's any agreement between themselves and Pascal. People talk about the wager as if the mercenary or gaming aspect of it is very bad. Well, that's just too bad. We're all philosophers here and we're interested in the validity of arguments. Not in whether they're tasteless or not. Or convenient, or have a good look and feel about them.

We want to know, nevertheless, whether it's a good argument, and talk about whether it's base or not is really not to the point. But in any case, Pascal is right, that... A very strong point in his argument is that you are forced to bet. The options are out there, and you're going to live your life one way or another. Given that your first forced to bet, you might as well think about it as betting, and think about the payoffs of the different courses of action open to you. That is rational.

Alan Saunders: But is he saying that one can come to... Supposing you take the bet, you decide that you're going to bet on God. Is he saying that you can come to believe something simply as a result of wanting to do so?

James Franklin: No, no. Many people have criticised the argument on that basis, saying that you can't decide to believe. Belief is not under control of the will like that. Either you think the evidence is one way or it isn't. But yes, Pascal is ahead of you there, because Pascal's, the conclusion of Pascal's wager is not belief but an action. Namely, going to mass and praying for faith. That is an action. And Pascal says it's up to God to do the rest.

That's part of his Jansenism, that he thinks that even with the... Even if the evidence was perfect that God exists, you couldn't gain faith; faith is a free gift of God, according to him. But, he says, your action is to go and make yourself open to that. So, I think he wins on that point again. He's not saying, the conclusion of his argument is not belief, but an action, namely asking for belief.

Alan Saunders: So, one way of putting it is to say that if you wager for God and God exists, then you gain everything. If you wager against God and God exists, the result will be misery. If God does not exist, then in both cases the result is essentially the status quo.

James Franklin: Yes. Well, Pascal says that if God doesn't exist then you will lose something by betting on him. Namely a more pleasurable life, but he says that's a rather small payoff. The difference in payoffs between a virtuous life and an unvirtuous life he says, at least for the sake of argument, is something, but it's not much, especially compared to the other option, that you might win an infinite payoff.

Alan Saunders: He's assuming, isn't he, that the probability of God's existence is 1 in 2. Is that reasonable?

James Franklin: Initially he says that he, you think of it as a heads or tails, and that's 1 on 2, but as he points out, it doesn't really matter what it is. If, because an infinite payoff will beat even a small probability. As long as the probability that God exists is non-zero, then the infinite payoff should counterbalance that and mean that you should bet for God. Because on the other side, there's only a finite difference in payoffs.

Alan Saunders: Is it right, though, to consider that there are only two possibilities to take into account in your wager?

James Franklin: That is the main objection, actually, to Pascal's wager that has been raised. That Pascal has not got straight the range of possibilities. Certainly Pascal does speak as if there are only two options, namely atheism and Catholicism of his variety. Now, that is quite right, that is a problem for his argument, but you have to remember two things. First is that Pascal is addressing a certain man of the world of 1660, for whom those are the two options.

Now, what about our situation? What about somebody else's situation? Well, we have a different range of options, but nevertheless the thinking of Pascal's wager still applies. Perhaps we have a much wider range of options, and we think that there could be lots of different religions with different probabilities of their being true, and perhaps we have a different opinion about the atheist option as well, and its probability. Well, it doesn't matter. The thinking of Pascal's wager is still right. The idea behind the wager is that you lay out the options that are live for you, and your subjective probabilities, what you think initially they're worth, and act accordingly. Which means probably for us we put research effort into finding which is serious.

So let's suppose we're in the situation of somebody brought up in an atheist or agnostic household that's never thought about religion. They get to their teens and start reading about these things and they realise there are religions out there, and they think, 'Well maybe I should think about these things.' I don't know, maybe... Why do people think these things? Probably somebody like that should think in Pascal's terms and say, 'Well, there's some non-zero probability that some world religion is right, but I don't know which. I should take out a book on world religions for dummies and start researching.' Yeah, that's the right way to think. It's not for me to say what the results of those researches may be, but that's what the wager says, I think, to the typical person of today; do some research.

Alan Saunders: So, the wager works even if I'm wagering not on God but on gods, on Vishnu and Kali and Ganesh for example?

James Franklin: Yes, if they're offering you payoffs, which they mostly seem to be doing, then you should do that. Perhaps you shouldn't bet on merely possible religions. I mean, some objectors to Pascal's religion have said that any guru could set up a religion with a suite of rewards and punishments and demand money from you, and actually as people think, perhaps scientologists and the like have done exactly that. But that is not a live option for you. Pascal's wager applies to the live options for the enquirer. And live option means you have some initial and substantial reason for thinking there might be something in that. So yeah, Vishnu counts, Mohammed counts, all of them count. The only person for whom Pascal's wager doesn't apply is the person who is absolutely convinced of atheism, and thinks that there's a zero probability for the sum of all options involving God. There are some people like that around, but that's not most people.

Alan Saunders: The French mathematician and philosopher Blaise Pascal applied probability theory to God in a work published after his death in 1662. And here's what he has to say:

'God is or he is not. Reason can decide nothing here. There is an infinite chaos which separates us. A game is being played at the extremity of this infinite distance, where heads or tails will turn up. You have two things to lose, the true and the good. And two things to stake, your reason and your will. If you gain, you gain all. If you lose, you lose nothing.'

And that's what I'm talking about this week with Professor James Franklin from the University of New South Wales. I'm Alan Saunders and this is The Philosopher's Zone.

But what about the possibility that God is not a benevolent God, but a malicious God? Or at least a bit of a divine awkward cuss? So If I choose to believe in him on the basis of a wager, he's not going to be too impressed.

James Franklin: Yeah, that is certainly something to be thought about. And especially since, as the people talking about the problem of evil insist, there is some reason to think that there is something cussed about God. Certainly if you look around the world, if it's his creation then there are some reasonable complaints about it. But when you think about what a malicious God implies, I think it doesn't imply anything about what you should do. Your first thought is probably that you should sacrifice a goat and hope he goes away, but who knows what a malicious God thinks about the sacrifice of goats? And if a malicious God has indulged in some revelations and told you what you ought to do, that still gets you nowhere, because a malicious God is a deceitful God. The devil is the prince of lies as they say, and there's no reason to believe that anything he says should be believed. So there is certainly a possibility that there is a malicious God, but it doesn't imply anything for action.

Alan Saunders: One of the things I find fascinating about Pascal's wager is that with it he is more or less initiating a number of areas of study. The psychology of religious belief, probability theory and of course decision theory.

James Franklin: Yes, a remarkable suite of achievements indeed. So, to just take decision theory which is perhaps the most famous outcome of his wager: Decision theory, of which this Pascal's wager is really the first instance, says that if you've got a range of options that you might implement, for anything from choice of life partner to where you should invest your money, you should think of the probabilities involved, like what might happen and how likely it is to happen, and then the payoffs, meaning the costs or benefits that are going to arise.

So that for example if you're talking about building or taking precautions about a nuclear plant, you have to think about the probabilities of something going wrong, which may be small, but weighted by the outcomes which may be a very large disaster. So, it's a very good perspective for deciding on what to do, to multiply the probabilities of outcome, by the costs and benefits that are going to arise.

Alan Saunders: And when it comes to another aspect of that trio of achievements, the psychology of religion, what he understands is that though you cannot will yourself to believe, you can and you've already more or less implied this, you can as it were put yourself in the way of belief.

James Franklin: That's right. You can, so to speak, prepare your mind for belief, which Pascal thinks is a free gift of God. Well, undoubtedly you can; you can do different things to, well, in the first instance you can go and find out about some theory and the reasons people have for believing it, and that will give you some way into whether it's a reasonable theory or not. And I think this is a very rational way to proceed in the question of choice of religion or for that matter, choice of philosophy.

First thing is, you've got to understand why people are thinking that way, and not just sit back and say, 'Oh, well, it sounds crazy to me, I don't know why those people are carrying on like that.' The rational decision is to investigate a worldview in an initially sympathetic way. It might turn out that when you investigate it you have a lot less sympathy than when you started if it looks awful the further you get into it. Still, first thing is some kind of sympathy.

Alan Saunders: I said he more or less initiated three areas of study, the one I hadn't mentioned is probability theory. Now, he's one of the founders of probability theory, but probability theory in his day was really about tossing coins or throwing dice. Probability theory is much more complex these days. Does the wager argument look different in the light of modern theories of probability?

James Franklin: I wouldn't say it did. I think it's turned out to be one of those things, as, like a lot of things in probability theory, where earliest... stacked up remarkably well. We know a certain amount more about probability theory, but it's still a very mysterious topic, probability. And in the light of the distinctions we now make, we now make a very strong distinction between logical or epistemic probabilities, which are about how you ought to think on the basis of evidence, like proof beyond reasonable doubt in law, which is about the relation between evidence and hypothesis.

Well, that's one kind of probability, and it's really the kind that's involved in Pascal's wager. And on the other hand probabilities of a stochastic kind, that deal with the chance outcomes of dice. So they, the chance outcomes of dice and coins form, in a certain sense, a model of other kinds of probability, but the logical kind is not always well thought about, is really about throwing coins.

Alan Saunders: But his notion of probability is that if you want to know what the probability of getting a heads is when you throw a coin, you just write a line on the page and you know the coin has two faces, so you write two under the line, and you want one outcome or the other, so you write one on the top of the line. And that's it, that's your probability.

James Franklin: Yes, that's right, so Pascal and his correspondent Fermat, those two genius mathematicians worked out the early mathematical theory of probability. They didn't connect it with long run relative frequency, like how much heads and tails actually come up. They did it in a very logical and abstract way, and they posed the problem in terms of, strangely a moral problem, the just division of a stake in an interrupted game.

So they asked, they said, two players have been playing, and they're forced to interrupt the game, and they're at a certain position, one is ahead of the other, how should they divide the stake? And they thought of that in terms of symmetry arguments, which are, as you just said, is basically about counting outcomes of different kinds. Well, that works well in a way, and it's certainly remarkable how well in many cases it agrees with what the coins actually do. There's perhaps certainly a little bit of a mystery about how talking about symmetry of ignorance, so to speak, actually works out in terms of how coins actually fall, but there it is.

Alan Saunders: What's your view of the standing of Pascal's wager as an argument today? As you've said, many people, atheists possibly even more than believers are somewhat disgusted by aspects of it, how would you say it stands today in the philosophical world?

James Franklin: Well, the majority of feeling in the philosophical world is certainly against it for the various reasons we've discussed; that it's disgusting, that it applies to anything. I think there's a lot of life left in it still, and I would like to see it taken rather more seriously, but it does need to be adapted to the space of hypotheses we have at the moment, which is much wider than the all or nothing atheism versus Catholicism of Pascal's day. But that's neither here nor there.

And I'd say in fact that it's more relevant now that we have more options, because the more options we have the more we need to think carefully about allocating our effort in researching them in the first instance, and if it comes to the point committing ourselves to them. Committing your life to a religion, or against a religion, is a very serious decision, just as in committing yourself to a life partner. We need to think very, very seriously about that. And the first thing to think is, where you should start. Where you should start thinking about putting your effort. Pascal's gives us the right decision theoretic framework for starting on that. We should go with him.

Alan Saunders: So the first thing we should commit ourselves to is serious thought and research.

James Franklin: Yes, that's right. And serious thought and research, first of all, serious thought and research on where we should seriously put thought and research. That's difficult, considering the chaos out there in the postmodernist world and the options we've got, but time to get straight, because it's very important.

Pascal makes the very good analogy with finding the deeds of a house, and, that perhaps will allow you to inherit a large property. And he says that you don't say to that, 'Oh, well maybe they're forged, I'll throw them away.' Well, that's a nice analogy for the young atheist who says, 'I think religions are all rubbish, I'm not going to investigate.'

Alan Saunders: Well, Jim Franklin, thank you very much for taking a bet on coming in here today.

James Franklin: Thank you.

Alan Saunders: James Franklin is Professor in the School of Mathematics and Statistics at the University of New South Wales. For links to his paper on Pascal's wager, and much more on the subject, check out our website, abc.net.au/rn/philosopherszone.

That's also the place to go if you want to tell us whether you'd bet on God. Or for that matter, whether you bet at all, and whether if you do your betting is governed by the calculus of probability.

And the music this week was by some contemporaries of Blaise Pascal, and it came from a favourite film of mine, Tous les matins du monde, starring Gerard Depardieu. The show is produced by Kyla Slaven, Charlie McCune is the sound engineer, and I'm Alan Saunders.