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Lesson 1.8: The Ace of Spades
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If we can’t prove whether God exists, should we treat belief like a gamble—and choose the option with the best payoff?
Topics discussed:
- The philosophical dilemma of whether belief in God should be based on reason, faith, or skepticism.
- Major positions on the existence of God: rational theism, fideism, deism, atheism, non-theism, and agnosticism.
- The life and intellectual background of Blaise Pascal, mathematician, theologian, and pioneer of probability theory.
- The historical origins of probability theory, including early work by gamblers like Gerolamo Cardano and Pascal’s correspondence with Fermat.
- The concept of expected utility and how decision theory evaluates rational choices under uncertainty.
- The structure of Pascal’s Wager, which argues that believing in God maximizes expected value because of the possibility of infinite reward.
- Mathematical objections to the wager, including the Many Gods objection and the Zero Probability objection.
- Psychological and ethical objections, including doxastic involuntarism, the moral integrity objection, and the Many Hells objection.
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Transcript
00:00:04
Speaker
Today we
Does God Exist?
00:00:05
Speaker
begin to pivot toward the philosophy of religion. And the main question we will wonder about is, does God exist?
00:00:17
Speaker
Now, there's many reasons why this question is relevant. ah Let's start with the first one. Some conceptions of knowledge that we've covered sort of rely on God, right? And that's what we talked about last time.
God in Empiricism and Rational Foundationalism
00:00:33
Speaker
We see God as being relevant, both in a kind of empiricism, the kind of empiricism that George Barclay advocates, but also Descartes' brand of rationalist foundationalism. So there's that reason for why we need to know whether or not God exists. But obviously there is a much um deeper reason, right?
00:01:01
Speaker
We want to know this. This seems like things that would be good to know, a thing that it would be good to know ah for you know our life.
18th-Century Theological Positions
00:01:12
Speaker
So we're gonna go into this debate And ah to kind of get our feet wet a little bit, i want to begin today by covering some possible positions on God's existence that were around in the 18th century, right? The 1700s.
00:01:30
Speaker
That is sort of the time period where we kind of left off. First and foremost, I should say that most people were still believers, right? They were still theists. That would be the the philosophical term for this.
00:01:46
Speaker
And quite a few of them were rational theists. What this means is that yes they had a belief in an all-powerful all-loving all-knowing creator right god but their view was that you can actually defend your belief in god through reasoned argument it is perfectly possible to come up with a good valid and sound argument to establish god's existence So that would be rational theism. Again, probably most people were still a theists and probably the majority of those people were rational theists.
00:02:26
Speaker
The minority view of theists was fideism. Now, fideism is a view that, you know, God does exist, but this is a matter of faith alone.
00:02:39
Speaker
Arguments will be insufficient for establishing God's existence. Rather, you just have to rely on faith and grace and that kind of stuff. So that is fideism.
00:02:50
Speaker
And this next view is sort of in the theistic camp. Like they sort of believe in a God, but it's not quite the God... of the Christians, right? But the deists or the deists, however you want to pronounce that, they did believe that there is a creator God, but not one that is all loving, right? This God created the universe and us and then just kind of left, right? And he doesn't listen to your prayers and none of that stuff. And so I'm not sure if you want to count these people in the theist camp,
00:03:27
Speaker
Because it's not exactly the kind of God that the other people, maybe have they have one foot on the theist camp. One foot in sort of like an a non-theistic camp.
Non-theism and Agnosticism
00:03:40
Speaker
But we'll get to that in a second.
00:03:42
Speaker
Let's also cover atheism. Sometimes I like to call this anti-theism because it really is anti-theism. Theism. It is a view that God does not exist.
00:03:56
Speaker
And we are getting the very first explicit outspoken atheists or anti-theists in the 1700s. Let me cover a view that is much more subtle now that was around but you know it's there's no good label for it so maybe people weren't kind of labeling themselves as such but i'm going to refer to it as non-theism this is simply the absence of a belief regarding god's existence
00:04:31
Speaker
Now, this is a very subtle difference. Okay, so the theist believes that God exists. The atheist believes that God does not exist.
00:04:45
Speaker
And the non-theist does not have a belief about God's existence. They neither confirm nor deny, right? Very diplomatic. um Some people...
00:04:57
Speaker
seem to have at least said that they were non-theists. Maybe David Hume counts in this camp. We sort of didn't want to, you know, say definitively either or or. Sometimes he would just kind of give in and say, okay, yes. But anyway, he might have been, you know, in his heart of hearts,
00:05:16
Speaker
either a non-theist or an atheist. We're not sure. But some other people, you know, it they have to, they kind of float around this view, right? It's like, I'm not really sure what I believe.
00:05:29
Speaker
I don't think i I have a belief on this. So that would be non-theism. And I have one more here for you. Agnosticism. Now this is different from both atheism and non-theism.
00:05:44
Speaker
The agnostic has a view about whether or not knowledge of God's existence is attainable. In fact, the agnostic says knowledge of God's existence is unattainable.
00:05:57
Speaker
That's something that you can't have knowledge about. right So they're not exactly skeptics about everything, but they are skeptics about whether or not you can arrive at knowledge of God's existence. That's just something that is beyond our capacities as human beings, says the agnostic.
00:06:17
Speaker
I do want to mention maybe these aren't quite positions on God's existence, but they are religious positions in general, sort of. so let's talk about two of these.
00:06:30
Speaker
Some philosophers and scientists during this time period saw the study of nature and just engaging in scientific discovery in general as a way to praise God's design.
00:06:44
Speaker
So they were some kind of theist, whether it be a rational theist or a fideist. And they really did see you know there their are scientific discoveries and their scientific work as an act of devotion to God, right? Very interesting position there.
00:07:05
Speaker
And that one doesn't cut across. I mean, you know, you can be either a rational theist or a fideist and engage in this kind of thing. Maybe even a deist. I'm not sure. But yeah, so that's one thing that you might ah believe or do.
00:07:22
Speaker
There's also a whole lot of religious reformism during this time period. So, you know, this is when the rise of biblical criticism comes about and some people really start questioning religious authorities and some religious people thought, okay, you're right.
00:07:41
Speaker
Traditional religion, the way we've been doing it for, you know, like a millennium, I guess, maybe need some updating, but we don't need to abandon religion altogether.
00:07:54
Speaker
And so these people were moving toward a more, i don't want to say progressive, but how about ah a moderate stance, right? And here, maybe you might think of the Calvinists or some kind of Protestant. They were moving toward, you know, um the religious was more so a private matter. And you kind of did that at home in that church. But the rest of the time, you know you were just a little bit more tolerant of disagreement. And um you know you there there was no need for you know being ah very ah zealous, right overly zealous. So just a simply more, um I don't wanna say laid back. That's actually not the right word either, right? But they're they're scaling it back a little bit.
00:08:40
Speaker
So that is a kind of religious reformism. And we do do see quite a bit of this in the 17 and eighteen hundreds as well.
Blaise Pascal's Dual Legacy
00:08:50
Speaker
And then there's the person we're covering today.
00:08:55
Speaker
Now, Blaise Pascal is little difficult to categorize. He is first and foremost a mathematician and then he spent the about the last decade of his life working on theology and he is very famous for You know, I wrote on here contributions to probability theory and projective geometry.
00:09:23
Speaker
Really, he is one of the co-founders of probability theory. So that's more than just a mere contribution, right? but But definitely one of the people that got the ball rolling here. And he is very famous for a set of arguments that we sort of collectively refer to as Pascal's wager.
00:09:45
Speaker
Now, Blaise Pascal during his lifetime was a mathematician, right? That's what he was known for. as a teenager, he was making massive contributions. But today we will be covering a work of his that was published posthumously.
00:10:03
Speaker
That means after his death. It is called Ponses, which means, I suppose, thoughts or meditations. and that was published in 1670 eight years after Blaise Pascal had passed away now this book Ponce's is not exactly meant for publication which is very interesting um what happened is that he started working on theology and he was going to you know publish a grand work on on you know basically establishing god's existence but he died at age 39 so he never got to complete this work and basically you know ah people that were familiar with his work
00:10:52
Speaker
took his pretty disorganized notes and sort of, you know, cobbled them together however they could. And that is what this book Ponce's is. And that is where we're getting the argument that we are covering today.
00:11:09
Speaker
Now I want to say a thing or two about Pascal as a human being for I guess two reasons. So let me let me tell you a little bit about Pascal and then I'll give you my reasons. But as I said, he was a mathematical prodigy and it is shocking what he was doing.
00:11:30
Speaker
He was apparently independently discovering or rediscovering, I guess, various geometric propositions as one would be able to find in a very famous mathematical text named the Elements of Geometry by a person named Euclid.
00:11:47
Speaker
Anyway, Pascal was doing this at age 12, right? So just imagine like a book that had been used for... over a thousand years that pascal had never read apparently and he was just you know independently you know coming to the same conclusions as uh as this super famous textbook in geometry that's blaze pascal um definitely ah a brilliant uh mind and it turns out by the time that he was only like 16
00:12:20
Speaker
He was producing mathematical works that really impressed his contemporaries in Paris, including one Rene Descartes, right? So clearly Pascal was, ah you know, set ah a fascinating mind, a beautiful mind, as you would say. And one more fun factoid about his productive years in the field of math and engineering he invented a type of ah of a mechanical calculator so that he can help his uh his father in his tax business and so that's fascinating right so not only pure mathematics but also applied mathematics blaze pascal truly a towering genius but
00:13:10
Speaker
In his early 30s at age 31, to be more precise, he had a mystical experience. That is, he had a religious experience where he seems to have you know undergone a second conversion, right? Everything was so clear to him. Abandon everything but God. God is the only thing that matters.
00:13:39
Speaker
And this second conversion shook him so much that he you know kind of wrote down a few, like a little brief description of this experience. And yeah, he after that, he just, you know, he changed completely. He stopped working on math by and large and shifted his focus primarily to theology.
00:14:03
Speaker
And so that was at age
Pascal's Mystical Experience
00:14:05
Speaker
31. As I mentioned, he died at age 39. So he spent the last roughly decade of his life working on theology instead.
00:14:15
Speaker
Okay, that's Blaise Pascal. Let me say, why we're covering Blaze today and why we're actually, you know, like it's kind of weird because he's from the 1600s. And so that's the first thing I want to touch on We are technically now in the 1700s, right? We just covered...
00:14:37
Speaker
Some arguments by David Hume. Hume died in 1776, right? The American Revolution was ah happening. And, ah you know, we also covered um an atheist, right?
00:14:50
Speaker
Baron Holbach, or at least I mentioned him. And he died in 1789, right before the French Revolution. So that's a time period we're covering.
00:15:00
Speaker
Why are we going backward in time over a century to cover Blaise Pascal? Well, Blaise Pascal is is important in the history of mathematics and philosophy and like society in general, because some of his methods for applying mathematics to like, you know, real life were incredibly influential.
00:15:31
Speaker
And that was all after his death. And so I want to give you a feel for what Pascal was all about, because a lot of people, as we will see in unit two, were really taken by, you know, the promise of mathematical methods. We can use math to figure like a lot of things out way more than we've been trying so far. Right. So so this idea,
00:15:59
Speaker
of of taking new mathematical methods and even inventing new mathematical methods like Newton did. He invented calculus um to figure out how things like, you know, society work um or what we should believe. Right. that That kind of starts with Pascal and maybe a couple of people before him, too.
00:16:21
Speaker
So that's why we are covering Blaise Pascal today.
Pascal's Influence on Mathematics and Decision Theory
00:16:26
Speaker
it is sort of to to emphasize the legacy of the kind of thinking that he engaged in. And so to talk about this legacy, I think it's time to get into story time.
00:16:43
Speaker
Okay, so I'm talking about math. Today is a very mathy lesson. So if we're going to tell this story, we're going to tell it correctly at least, and we're talking about in particular probability theory and something called decision theory, we technically have to go back even further to the 16th century to the time period of a man named Gerolamo Cardano.
00:17:13
Speaker
Now, full disclosure, Cardano was ah a doctor, right? A physician, but he was also a gambler. In fact, I think he had a gambling problem.
00:17:25
Speaker
in any case, um it just has to be said that the field of probability theory or the beginnings of what would become probability theory just has some relationship to gambling, right? To games of chance. It is what it is, right? We just have to say that.
00:17:47
Speaker
And so in the 1500s, Cardano publishes the book on games of chance. And this is one of the first attempts to reason about randomness mathematically.
00:18:01
Speaker
he used intuitive ratios to think about fair bets. long before the field of probability existed. Now this is very much in the spirit of the Age of Enlightenment, which is again in the 1700s. That's why it fits in so well with the story that we're telling.
00:18:24
Speaker
These ah budding probability theorists were way ahead of their time, like 200 years. ahead of their time. The best way I can make this argument for you, I think, is by telling you about what people thought about luck.
00:18:41
Speaker
in the 1500s and earlier. Before Cardano, people thought of luck as divine intervention or just fate, you know.
00:18:52
Speaker
And Cardano was the first to realize that you could map out every possible outcome of a dice roll and that while any single roll is random, right, if you just roll the dice once, that's random.
00:19:06
Speaker
the ratio of outcomes becomes predictable over a long period of time. And so what Cardano was really doing is moving from the supernatural explanation of a dice roll, let's say, a natural explanation of a dice roll.
00:19:30
Speaker
He was, in other words, engaging in a sort of naturalism about luck. Now, that is exactly what the Enlighteners were doing in the Age of Enlightenment. They wanted to explain things like, you know,
00:19:46
Speaker
why someone is acting erratically, they explained it in terms of like a mental illness instead of demonic possession. That just is being a naturalist about you know mental states, I suppose, or mental disorders.
00:20:03
Speaker
And so this is what Cardano was doing about games of chance in general. So that starts in the fifteen hundreds We fast forward a bit to 1654.
00:20:18
Speaker
And apparently someone asked Blaise Pascal, of course, brilliant, to famous for you know ah for his mathematical contributions.
00:20:28
Speaker
They asked him, hey, how do you fairly divide the winnings of a game that ends early? So you're playing you know your game of chance, whatever it is. And i don't know, something happens. There's a fire, whatever.
00:20:40
Speaker
and so you have to leave early but you haven't you know it's not over so how do you divvy up the winnings right who gets what well pascal reached out to a very famous mathematician named pierre de fermat and of course uh pascal was incredibly famous himself so you know he reaches out to another famous mathematician they will respond uh he knows him So they began engaging in ah correspondence about this and their solution to this this question about how to fairly divide the winnings of a game that end early.
00:21:19
Speaker
You can see it in their letters, right? It introduces a new mathematical idea and this is often seen as the birth. of probability theory.
00:21:30
Speaker
So that is, you know, it's kind of funny because this this thing about games of chance just kind of keeps cropping up in the history of ah probability theory.
00:21:43
Speaker
In any case, Pascal ah goes further, of course. it's It's just like Pascal to take an idea and go all the way, see see where it takes you, right?
00:21:55
Speaker
So, of course, in the last decade of his life, Pascal was working on theology. And so with probability theory in hand, Pascal tries to take this idea as far as it can go.
00:22:07
Speaker
If probability tells us the likelihood of an event, decision theory tells us about the rationality of a choice. So what Pascal does is decides to use some elements of probability theory to come up with something that we now call expected value theory,
00:22:32
Speaker
which is a part of decision theory. Now, because it was the first part of decision theory that was invented, I'm just going to call it decision theory.
00:22:43
Speaker
Here is what expected value theory basically says. If you want to know what, how, let's just say how rational a choice is, you basically put all your choices together and to figure out the expected value of each one,
00:22:59
Speaker
You multiply the probability of winning with the value of the win and subtract from it the probability of losing and the cost of the loss.
00:23:12
Speaker
Now, if that doesn't quite make sense to you, don't worry. We're going to go over a few examples right now.
Introduction to Pascal's Wager
00:23:21
Speaker
so why are we doing any of this well the main reason is that we're going to go over something called pascal's wager now it sounds singular but it's it's not uh it's actually it's a whole series of arguments to be honest so i'm going to define this as an umbrella term referring to a family of arguments given by pascal Stating that, roughly, it is best to believe in God since the possibility of eternal reward outweighs any possible disadvantage brought on by believing in God.
00:24:05
Speaker
put another way, he basically says that it's the most rational thing to believe in God and he will show you through this thing he came up with basically called decision theory or expected value theory.
00:24:22
Speaker
So that is what we are covering today. And in order to show Pascal's argument, we're gonna focus on his third argument in this series of arguments.
00:24:35
Speaker
We're going to learn how to build something called a decision matrix. A decision matrix in decision theory is a table intended to help one discover the expected utility of a choice.
00:24:50
Speaker
There's rows, they go left from right, left to right, and they correspond to the possible actions that you might take. And then there's columns. They go up and down and they correspond to the possible states of the world.
00:25:07
Speaker
Each cell that is created when these rows and columns intersect represents the utility of an action given a particular state of the world.
00:25:19
Speaker
So you probably need an example and I'm happy to give it to you. So let's just define utility. The utility of a possible action is a numerical value assigned to the outcome of that action.
00:25:34
Speaker
These are given to all possible actions so that one can juxtapose them. They go in the rows of the decision matrix and are aligned with the possible state of the world that would produce utility.
00:25:47
Speaker
So here is a decision matrix that we will fill in together. Let's say someone goes up to you and says, all right, let's play a coin toss game.
00:25:58
Speaker
And if it lands on heads, you get two bucks. But if it lands on tails, you give me two bucks. So there's two possible states of the world in this game.
00:26:09
Speaker
I hope that's clear. Heads, tails. And those go in the columns. Now you have two choices here. You can either accept to play this game or you say, no thank you. I don't really wanna play that.
00:26:24
Speaker
So you don't play. Okay, let's say that you play. We have to fill in the utility here on the cell that that that corresponds to each state of the world given your action. So let's just say you choose to play and it lands on heads. Then we give this a utility of two.
00:26:43
Speaker
which represents the $2 you will make if you if you win, if it lands on heads. And if you play but it lands on tails, you lose $2. That's negative two.
00:26:56
Speaker
I use negative numbers, by the way. Pascal didn't, but that doesn't matter. We all know what negative numbers mean, so... There you go. Now let's just say you don't play. This is actually a very nice and easy row to deal with. And I would typically keep keep one of the rows pretty simple. If you don't play, it it just like nothing happens, right? Just zero.
00:27:18
Speaker
So don't play it lands on heads, you get zero because you're not playing. And don't play it lands on tails, you get zero because you're not playing, right? So there you go. That is your decision matrix. Now you can add a new column if you'd like to calculate the expected utility.
00:27:39
Speaker
So what you do for that is you take each utility and you multiply it by its probability and then you add the numbers together. So ah the probability um of you winning, right, times what you get and the probability of you losing um times is what you get if you lose, right? And then you get the numbers together.
00:28:02
Speaker
So we need an example. Let's just do this right now. Another coin toss game. In this one, you win a dollar if it lands on heads and you lose a dollar or sorry, you lose two dollars if it lands on tails.
00:28:16
Speaker
Okay, let's generate the decision matrix. You got your heads and tails on the columns. You got play, don't play on the rows. And we need to fill in the utilities. If you don't play again, that's the easy row. It's just nothing happens, right? Zero.
00:28:33
Speaker
If you play, it's plus one, right? $1 for heads and minus two or negative two for tails. Okay.
00:28:46
Speaker
As I mentioned, I'll keep one row nice and easy this whole time. If you choose not to play, we'll call that choice X. ah The expected utility is zero because yeah, zero times whatever is zero plus Zero times whatever is also zero. So just zero, right? So ah that one's the easy one.
00:29:07
Speaker
Let's call the choice of playing choice y And for that one, we do need to engage in some math. Now, typically, maybe if you do it in your head, you can just add another column to your decision matrix.
00:29:22
Speaker
I'm going to do the math on the side here so you can really see. a lot of people don't like math, so going to do it on the side. Hopefully it's more obvious to you this way. So what we do is we take the utility. We're we're doing, of course, the row where we're playing.
00:29:39
Speaker
We take the utility, if it lands on heads, which is one, and we multiply it by the probability that it will land on heads, which is 0.5, right, 50%. So that's the part to the left.
00:29:52
Speaker
And ah you also need to take the utility of it landing on tails, which is negative two. And you multiply that by the probability that it will actually land on tails, which again 0.5. And there you go. 0.5 times one plus 0.5 times negative two.
00:30:10
Speaker
point five times negative two So you do some math here and 0.5 times one is just 0.5, right? And 0.5 times negative two is negative one.
00:30:24
Speaker
Cool, so far so good. Now we're gonna add those numbers together. which essentially means 0.5 minus 1 right here. So what we end up with is negative 0.5.
00:30:38
Speaker
In other words, choice Y has a negative utility, right? Negative 0.5. That is not good because I'm going to blow your mind right now.
00:30:52
Speaker
0 is greater than negative 0.5. You thought I bet that doing all those inequalities in like seventh grade or whenever you did it, i don't know, it was never going to be ah useful. Well, here it is. it turns out.
00:31:09
Speaker
that through this decision matrix you realize that playing this game is definitely a bad idea it is a losing game in the long run and so what should you do if
Decision Theory Explained
00:31:22
Speaker
someone goes up to you and offers to uh you know play this game with you you say no that would be the right thing to do there you go decision theory at work right Awesome, let's do another example because I know that usually takes a bit before people grasp what is going on here.
00:31:44
Speaker
And let's make it a more modern example. Someone goes up to you because they know that you have a spare thousand bucks and you don't know what to do with it. So you have this opportunity to invest in a tech startup. Now it is a high risk startup.
00:32:03
Speaker
So you have, let's just say, i'm oversimplifying here you have two options choice x we're gonna make the it the easy one again you just put your money in a safe all right not not a bank account or or anything like that then we have to do like interest rates and we're not doing that we're keeping it easy here you just keep your money in safe that's choice x awesome by the way we already know the expected utility of that is zero right uh it won't go up it won't go down it's going to stay a thousand bucks
00:32:36
Speaker
Cool. Choice Y now is the more complicated one. You can invest your $1,000. Now you need the information ah about what is likely to happen.
00:32:49
Speaker
And you consult with a bunch of people, you end up discovering that there is a 10% chance that the company goes public. And oh my goodness, if that happens, you gain $20,000, right?
00:33:01
Speaker
twenty thousand dollars right That's pretty pretty good However, there is a 90% chance, way more of a chance that it will fail and your $1,000 becomes zero, right? You lose your $1,000.
00:33:21
Speaker
What should you do? Should you keep your money in the safe or invest your $1,000 X or Y? Well, X, as I said, the expected u utility is zero. Y, let's do some math here.
00:33:36
Speaker
We take your the utility of ah investing and the ah the company going public, which is 20,000, and multiply it by the probability of that actually happening, which is 0.10, right, 10%.
00:33:52
Speaker
And then you take the utility of the company failing, which is you losing your $1,000, negative 1,000, and multiply that by the probability that that's what's going to happen which is 90 or 0.9 and then you add the numbers together so uh for the first amount it is 2000 and the second one would be negative 900 Then you do a little more math and you realize that the expected utility of choice y is 1100, right? So choice is 1100.
00:34:29
Speaker
the expected utility of choice x is zero and of choice y is eleven hundred What's your decision? um Well, I know that some of you might be risk averse, but the whole point of decision theory is to figure out what is most rational to do, right? Taking emotions out of the equation.
00:34:55
Speaker
And so the decision here would be, well, since 1100 is greater than zero, you should invest, right? That would be the rational thing to do.
00:35:07
Speaker
Well, this is all fine and good. and as we saw, it's definitely the case that mathematics um is very applicable and is considered very applicable during this time period.
00:35:24
Speaker
But Pascal does something different. And, you know, he's not going to just... leave it at, you know, whether or not you should invest or not, right?
00:35:35
Speaker
He takes this idea and he applies it to something that is, well, you know, it's a matter of life or death in a way,
Applying Decision Theory to Belief in God
00:35:46
Speaker
right? He's going to take the notion of expected value and apply it to the question of whether or not you should believe in God.
00:35:59
Speaker
So let's turn to that now.
00:36:39
Speaker
Before we get into the argument of the day, do want to say something about the way Pascal's philosophy is usually ah transmitted or taught.
00:36:55
Speaker
People typically focus on Pascal's wager, and in fact, just in one of the arguments of Pascal's wager. um to be honest, I think that Pascal's work is much richer than that, than the way that we treat it. Although I am guilty here.
00:37:15
Speaker
i am just like ah my philosophy teacher, only covering one argument from Pascal, but there is so much more to him, he wrestled with both the radical skeptic and what he saw as the dogmatism of Cartesian foundationalism. So he didn't like Descartes.
00:37:37
Speaker
He also didn't like, um well, I was going to say the Pyronian skeptic, but really, Pascal read the work of a man named Michel de Montaigne, who was heavily influenced by Pyronian skepticism. And it seems like Blaise Pascal was literally...
00:37:57
Speaker
read a couple of pages from Montaigne and then run to his notebook and like, you know, write his response down. So he really was in ah in a serious way responding to something like Pyronian skepticism.
00:38:13
Speaker
And so, you know, there's all those aspects of his philosophy. There's also a whole lot of like pragmatic or practical philosophy because he thought hard about how do you how do you human, right? How do you life? What it means to be a human. And he was fascinated by how we are capable of both great sin and great virtue.
00:38:37
Speaker
And he really saw some of what he was doing. in using mathematical methods and applying them to everyday context, he saw it as sort of what we have to do because we are cognitively degraded by original sin. So according to St. Augustine from the you know four hundred s ce Original sin kind of makes us a little dumber, a little less free, a little less rational. Right. And so and we're all we're all guilty of that. And Pascal believed that. And so that's why he used mathematical methods. Right. To help us get over those sort of built in weaknesses. Right.
00:39:24
Speaker
I don't know, I find the whole thing fascinating and I didn't want to, you know, pass over ah the the rest of Pascal's work without mentioning something about it.
00:39:36
Speaker
But now, just like my teacher did before me, here we go Pascal's third argument from the Ponces. And here we go.
00:39:48
Speaker
Let's see how this goes. First and foremost, he begins with an axiom, right? Hopefully something that you find intuitive. You should choose the action of maximal expected utility if there is one.
00:40:05
Speaker
That just basically says that once you fill out something like a decision matrix, right, and you compare all your options, you should probably go with the best one for you, right? um It seems counterintuitive just counterintuitive to say something like, yeah, go for the second best. I mean, why?
00:40:25
Speaker
just choose whatever is best for you. So that's sort of an axiom, an intuitive truth, if you want to call it that. Let's get into the rest of the argument.
00:40:37
Speaker
Here we go. The probability P that God exists is positive.
Probability of God's Existence
00:40:44
Speaker
Pascal says something like, well, you know, I'm not going to give a number to the probability that God exists, to the proposition that God exists.
00:40:58
Speaker
Typically, probabilities go between zero and one. Zero means it's for sure not gonna happen. One is you know a certainty. And you know like a coin toss is 0.5, right? It can go either hedge or tails.
00:41:11
Speaker
So if you are going to say something like God exists, you can assign a probability to that. And Pascal basically refuses. He says, well, you know, it's it the human mind too too weak, too tiny.
00:41:25
Speaker
i Can't figure that out. But he does say it is a positive number. And so maybe you can imagine Pascal sort of envisioning an atheist. And I'm sure atheism was not that common when Pascal was around. But if you just imagine a radical skeptic, um,
00:41:47
Speaker
Pascal is trying to convince a skeptic, like, even if you, you know, find it very unlikely that God exists, you can still leave a little bit of room for you being wrong, right? So even for an anti-theist, Pascal is trying to convince him, maybe set your probability that God exists at 0.00000000001, right? It's a very small probability, but it's still a positive number. And basically it's not zero.
00:42:23
Speaker
So another way to state premise two is there is a non-zero possibility probability that God exists. So hopefully this convinces anyone other than the dogmatic atheist, the atheist that just says, no, I don't believe in God at all. There is zero chance that God exists.
00:42:44
Speaker
Pascal would say, well, that's really unreasonable. Like you don't know everything. There's got to be at least a small chance that you're wrong. You've been wrong before, right? So... That's sort of the idea behind this second premise. There is a non-zero chance that God exists.
00:43:03
Speaker
Okay, then he, well, we are going to set up a decision matrix sort of like this. And in this um decision matrix,
00:43:16
Speaker
We're gonna have F1, F2, and f three What does that mean? Those are finite amounts, right? So F1 is some number and it's just not infinity, right? Maybe it's a billion, maybe it's a hundred, maybe it's two.
00:43:33
Speaker
It's not infinity, right? Same thing for F2. It's another number, but not infinity. And F3, right? These are all non-infinity. So let's let's fill this out. It'll be clearer when we do.
00:43:45
Speaker
There's two possible states of the world. God exists and God does not exist. Okay. Easy peasy so far, right? On the matter of whether or not you should believe in God, you basically have two choices.
00:44:01
Speaker
You could say believe in God or don't believe in God the way Pascal would say is wager for God or wager against God. Those are your options.
00:44:14
Speaker
Now, let's say that you wager for God and God exists. Yeah, that means that you bet right, right? And you get to go to heaven.
00:44:26
Speaker
And so that is an infinite reward, right? That is heaven forever, eternal bliss, whatever it is that heaven is for you. That's yeah, heaven, infinite.
00:44:39
Speaker
Okay, that's the easy one. Now we have these other options. If you wager for God, right, you're a good Christian your whole life, and it turns out when you die that you just die and God doesn't exist.
00:44:54
Speaker
Well, you know, he says maybe it's a positive. Maybe it's a negative, right? Maybe it's a lot of work to be a Christian. Maybe in the end of your life, it ends up being something like a negative 100. That kind of sucks.
00:45:09
Speaker
Or maybe it wasn't a bad life, right? You had some good luck and you ended up with a positive 5,000. What Pascal is going to say here is that it doesn't really matter what number it is or even if it's positive or negative.
00:45:26
Speaker
It is a finite number. It is not infinity, in other words. And so, yeah, it's just either good or bad, but not infinity. Okay.
00:45:37
Speaker
Well, what if you wager against God? you You just say, yeah, you know, I don't think God exists and I'm gonna live my life like that. And it turns out that God exists. You would expect that you would get something like negative infinity, right?
00:45:53
Speaker
Well, you know, i don't want to get into the whole hell thing right now but throughout Christian history, there's been all kinds of different beliefs about hell. And Pascal, at least in this argument, has an unconventional view.
00:46:08
Speaker
ah Pascal believes that God isn't going to punish anyone for all eternity if you don't get into heaven and, you know,
00:46:22
Speaker
for whatever reason basically pascal says that god is going to simply extinguish you you will you will no longer exist right your soul goes away for good like it's just done no no torment no hell just non-existence and so what that basically means is that you live your life and maybe it was a good life right positive 10 000 maybe it was a bad life negative 10 000.
00:46:49
Speaker
it doesn't really matter for Pascal because his point is that it is a finite amount and because you stopped existing what you're yeah that's it you're done right there's it's over it's finite so That's F2.
00:47:06
Speaker
And something very similar is going to be said about the case when you wager against God, right? And God doesn't exist. Technically, I guess you were right.
00:47:18
Speaker
And so you lived your life as a non-believer and you died and you were right. and You just die. and And then your life is whatever it was. Maybe it was positive 2 billion, whatever.
00:47:28
Speaker
Or negative five, it's still a finite amount. So Pascal is making a big kind of ah assumption here, but it's pretty key.
00:47:40
Speaker
Only one of these cells gives you an infinite utility. right If you wager for God and God exists, that is an infinite ah utility. And so that is the only one that has that feature.
00:47:58
Speaker
Now, if you were to be you know a mathematician slash logician who is studying the history of math and logic, ah the next part of the passage is sort of going to blow your mind because in this passage from the Pensees, essentially Pascal invents expected utility theory, right? And thereby invents decision theory.
00:48:27
Speaker
So here we go. We're going to geek out for a second here. These are lines from Alan Hadjik, who is a mathematician, logician, and historian of those fields.
00:48:39
Speaker
So here's a quote from the gentleman. In another landmark moment in this passage from the Ponses, he next presents a formulation of expected utility theory.
00:48:53
Speaker
When gambling, now quoting Pascal, every player stakes a certainty to gain an uncertainty, and yet he stakes a finite certainty to gain a finite uncertainty without transgressing against reason.
00:49:11
Speaker
So what does that all all that mean? It's actually what we've been talking about this whole time. it just said Pascal uses different language. um But he's talking about how you can make guesses within complete information and still be rational, basically.
00:49:30
Speaker
So let me continue here with a quote. How much then should a player be prepared to stake without transgressing against reason? Pascal's answer.
00:49:41
Speaker
The uncertainty of the gain is proportioned to the certainty of the stake according to the proportion of the chances of gain and loss.
00:49:53
Speaker
Now, if that sounds like word salad to you, ah even Hajek, the guy we're quoting, says the same thing. So let me close off this quote. It takes some work to show that this yields expected utility theories answer exactly.
00:50:10
Speaker
but it is work well worth doing for its historical importance. In those passages, as he is outlining this argument, Pascal invents expected utility theory and thereby invents decision theory.
00:50:29
Speaker
So, i mean, I don't know. That's that's pretty mind-blowing to me. Maybe not mind-blowing to you. So let's continue with the argument and see if we can get some minds blown somewhere.
Expected Utility Theory in Ponses
00:50:42
Speaker
Premise four. therefore wagering for God has infinite expected utility so let's look at the math here first we have to take the utility of ah you know what what happens if we wager for God and God actually exists as we decided earlier it is infinity and we have to multiply that by the probability that God actually exists We don't know that number, so we're going to just put in P there.
00:51:17
Speaker
But notice that any number times infinity is infinity, so that amount is infinity. And we add to that...
00:51:29
Speaker
What happens if you believe in God, but God doesn't exist? Remember, we didn't have a number for that. We called it F1. But now you take F1 and you multiply that by the probability of it actually being the case.
00:51:46
Speaker
We don't know that number either. So what we're going to do is multiply it by 1 minus P, right? So whatever you decided the probability of God existing is, you subtract that from 1 and that's the probability that God doesn't exist, right? Because all probabilities are between 0 and 1.
00:52:05
Speaker
But again, it actually doesn't matter because any number plus infinity is still just infinity. So no matter what, because infinity is the utility for at least one element of that row, the expected utility of believing or wagering for God is infinity.
00:52:30
Speaker
That is a result. ah It's basically what happens when you have infinity as one of the utilities. And therefore, given that infinity is greater than any finite quantity, you should wager for God.
00:52:49
Speaker
And so here is an updated decision matrix. And I added a column here for the expected utility on the right. And the expected utility for wagering for God is infinity.
00:53:04
Speaker
And if you wager against God, well, I don't know the number. so I just put finite quantity for, right, F4. But it doesn't matter. infinity is greater than any finite quantity and so the best choice simply is to wage for god right did that blow your mind infinity is greater than finite quantity four
00:53:36
Speaker
Okay, sometimes people don't know how to feel about this argument until they look at some of the objections.
Criticism of Pascal's Wager
00:53:44
Speaker
These objections are, ah I don't know, fun, famous, they're cool.
00:53:49
Speaker
I basically divide them up into two camps, mathematical objections, and the other one's more like I don't know, psychological slash moral objections. It's kind of weird camp, but let's look at the mathy ones first.
00:54:05
Speaker
Let's begin with the many gods objection. Now, this objection points out a very obvious maybe problem with the decision matrix that we've been exploring. There's a bunch of other competing religions.
00:54:21
Speaker
And at least some of those religions are worthy of some probability in the decision matrix. In other words, you know, we're missing things like, you know, Islam and Judaism and whatever.
00:54:35
Speaker
And so the row, sorry, the decision matrix, It just needs more rows in it, right? That would mean that there's multiple possible routes to infinite expected utility. Some of these rows would have in their decision matrix infinity as utility, which means that they would also have infinite expected utility.
00:54:59
Speaker
um If that's the case, choosing Christianity is not as straightforward anymore, right? There's quite a few choices that yield the exact same expected utility.
00:55:12
Speaker
And so you need a reason for choosing Christianity over, for example, Hinduism or ah Islam or Judaism or whatever, right? doesn't matter. Any religion that gives you infinite expected utility. I have here an updated um decision matrix and we added a slot here for Islam and Judaism and Hinduism and past the foreignism whatever right put in whatever religion you want in there that promises infinite reward and it complicates the the the final choice quite a few ah religions have an expected utility or yield an expected utility of infinity
00:55:55
Speaker
So that is one objection that, you know, essentially little more mathematical than anything. There's also the zero probability objection.
00:56:08
Speaker
So you might get like a hardcore atheist or anti-theist who argues against premise two. They basically might claim that the probability of God existing is actually zero.
00:56:21
Speaker
Maybe they say that literally the idea of God is internally incoherent, which means that it's impossible, which means that the probability of such a being existing is zero.
00:56:36
Speaker
In that case, the expected utility would be zero because infinity times zero is is zero in fact any number times zero is zero and so it makes no sense at all to wager for god you're better off um going for whatever finite quantity just try to make it a positive one so there you go not uh um
00:57:06
Speaker
agreeing with the probability that Pascal assigned to God's existence. By the way, that kind of argument or objection, I should say, would affect any other religion ah that has a sort of a, you know, Judeo-Christian model for God in it.
00:57:24
Speaker
So maybe quite a few of these rows would end up with an expected utility of zero. Okay, so much for the mathematical objections.
00:57:38
Speaker
Let's and move into, um you know, to be honest, some of these are more intuitive to some people. They're more like psychological objections. Although I do have ah something to say about morality as well.
00:57:51
Speaker
But let's begin with, I hate this name for this view, but it is what it is. So the doxastic involuntarism objection. So if I were to go up to you and say, hey, you know, I will pay you a billion dollars if you believe the sky is green.
00:58:07
Speaker
You know, it's it's not going to be easy. One cannot simply decide to believe that the sky is green just because someone offers them a million or a billion dollars, right? Belief requires being convinced by evidence. It's almost like belief is not exactly under our control. It's a product of what we see and hear and learn and think about.
00:58:32
Speaker
And you can't like entice it with a payoff. And so at least about things that matter. And so it's not clear that you can just say, well, you know, I made my little decision matrix and it says I should believe in God. So now I believe in God.
00:58:48
Speaker
that That just doesn't seem to work, right? So funnily enough, you can go through Pascal's writing and find his counter. He actually said, okay, that's absolutely the case.
00:59:02
Speaker
But you should act as if you do believe. And eventually your mechanical habits, you just kind of going through the motions will tame your skeptical mind and you will eventually actually accept God, right? Believe in God.
00:59:19
Speaker
So fake it till you make it is basically Pascal's counter here. But yeah, that's that's an important objection. it's It's not clear that Pascal's psychology is accurate. Maybe his idea of what the human mind is capable of believing is not really you know, what we now share intuitively, what we we think of when we think of our human psychology. In fact, I have a friend who is an anti-theist, right, an atheist.
00:59:50
Speaker
And he acknowledges that there's lots of benefits to religion, like community, like ritual, like a bunch of things. And he has told me like he wishes he could be religious.
01:00:02
Speaker
but he can't, right? So maybe that's a real knock on on Pascal's argument here. Okay, this is called the moral integrity objection.
01:00:17
Speaker
You know, it just seems like an all-knowing, all-loving God would absolutely not be impressed by someone who just believes in him kind of as an insurance policy, right? It just seems so mercenary.
01:00:33
Speaker
And obviously, because God is all knowing, he would just see right through you, right? He would be like, yeah, you don't get in here just because you pretended to believe or you believed because you did some math. Like that that's not that's not how it works.
01:00:50
Speaker
And so there's just something, ah i don't know, disingenuous about this approach maybe. Okay, another interesting objection, maybe my favorite objection is the many hells objection. um i don't know, it just I think I just wanted to put an image of fire on my slides.
01:01:13
Speaker
Most religions, they don't just require belief in a God, right? They require specific rituals and dogmas and all that, but most importantly, the rejection of other sects, right? You have to deny the truth of other religions. that That's sort of a mandatory aspect of a couple of religions that I can think of.
01:01:37
Speaker
So If you are, you know, ah doing the math here and and you're trying to figure out what happens if you wager against a specific religion, well, Pascal put in there a finite amount because he kind of had a view about hell where it doesn't really exist, right? You just kind of stop existing.
01:02:00
Speaker
But that's not what other religions say, right? According to other religions, there is a hell. So if you bet on the wrong version of Christianity, like a version of Christianity that actually has a hell, or Islam, or Judaism, or whatever, right? Any religion that has a hell, they actually...
01:02:19
Speaker
have a negative infinite utility on there. And so you might still end up in a version of hell. So how do I say this as succinctly as possible?
01:02:32
Speaker
In reality, there's hundreds of religious options, right? you know i was gonna say and an earlier version of these slides, I said dozens, really there's like hundreds of them.
01:02:42
Speaker
And at least some of them carry the potential of negative infinite utility. And so that means that some rows in your decision matrix have an expected utility of negative infinity.
01:02:59
Speaker
How do you make that choice? Now you're saying, OK, well, these give me a positive infinity and these give me negative infinite and negative infinity.
01:03:09
Speaker
OK, you don't take that choice very lightly, I hope. You're not just gonna go for one of the infinities like, yeah, that one's fine. Because if you do the wrong thing, if you choose the wrong religion, you might end up in some version of hell.
01:03:26
Speaker
So the decision matrix, in other words, is incomplete and insufficient to actually help you arrive at a rational choice, given that if you mess up, you might end up in hell.
Safety vs. Truth-Seeking in Belief Decisions
01:03:42
Speaker
All right, well, These are some pretty serious objections, but wanna close with maybe a less clear objection. I hear this sometimes when people discuss Pascal's work, either at an academic conference or even in class. Some people say something like,
01:04:06
Speaker
If we use math to decide what to believe, haven't we abandoned the pursuit of truth in favor of the pursuit of safety? That's one kind of objection that I've heard. It's not exactly an objection, right?
01:04:19
Speaker
It's more so a question, but there's something about the the strategy that doesn't sit well with people. And it's a form of like safetyism, if you want to call it that.
01:04:33
Speaker
And it just doesn't sound good. it doesn't seem like it puts your you know your the the right values forward. Another thing I've heard is something like, does the wager actually save the soul, right?
01:04:49
Speaker
Or does it provide just some kind of logical excuse for those who are afraid to doubt? This sort of objection typically comes from someone like an atheist who said something like, you know, these people are so afraid to doubt in God's existence that they come up with these mathematical workarounds so they can still believe.
01:05:12
Speaker
Yeah, well, I don't quite think that ah these, again, these aren't even objections. or' just questions that I put up here, but I've heard something like them.
01:05:24
Speaker
And let me close by saying that I don't think that these criticisms of Pascal's wager are I don't think they really are quite fair because the work, you know, the Ponce, as I said, was unfinished.
Pascal's Personal Faith Journey
01:05:43
Speaker
So he never got to say what he wanted to say. Remember, it wasn't decision theory that brought Pascal to his ah quote unquote second conversion.
01:05:58
Speaker
The way that he arrived at his views was through a mystical experience. And in closing, i want to mention that a little bit.
01:06:11
Speaker
Apparently he had some vision of God and it took about two hours. When he was done, he wrote a brief record of it and a little note.
01:06:23
Speaker
And this note was very important to him. After he wrote it, Pascal folded the the note very carefully and he did something very strange.
01:06:36
Speaker
He sewed it into the lining of his coat and he carried it around with him everywhere he went for eight years until the time of his death.
01:06:50
Speaker
And no one knew it was there. When Pascal died in 1662, a servant discovered the note hidden inside the coat.
01:07:03
Speaker
So it was a secret that he had carried since that mystical experience. A reminder of the night he believed he encountered something beyond reason.
01:07:16
Speaker
So it turns out, the mathematician who helped invent probability theory spent the last decade of his life haunted by a moment he could never calculate.