Pascal’s Wager

Rene DesCartes and Blaise Pascal lived in France about 400 years ago. They were colleagues and they were both mathematicians. Also, they both tried to prove the existence of God.

Rene DesCartes tried to prove it directly, arguing that nothing can exist without God. But his attempt failed; he only got as far as proving that you can’t ask questions if you don’t exist. This is usually summarized as Cogito Ergo Sum, which I discussed in my last post. If you ask me, his attempt was doomed from the start; it’s just too long a chain of ideas and each link in the chain can break very easily.

In order to justify a claim like “You need to believe in Jesus in order to get into Heaven”, you’d have to show all eight of the following: #1 There’s a law which says everything has to come from somewhere, e.g. if you see a shoe, there must have been a shoemaker (Let’s call this the Shoemaker Law). #2 The Shoemaker Law applies to the universe itself. #3 The Shoemaker Law does not apply to whatever created the universe. And whatever created the universe… #4 is able observe what happens as the universe unfolds, #5 cares deeply about the behavior of the creatures which inhabit the universe, and #6 has a plan for rewarding or punishing those creatures based on their behavior. Also, #7 You know what the rewards and punishments are. Finally, #8 You know specifically which behaviors are the ones to be rewarded and which ones are to be punished.

Cogito Ergo Sum doesn’t prove any of the links in that chain, let alone all of them.

In modern times, others have tried to build on DesCartes’s work by making the dubious claim that the Shoemaker Law applies not only to the universe, but to knowledge and logic itself. Their argument is basically “I think, therefore logic is real, therefore God exists”. At best, this allows them to bypass the first three links in the chain I described above. But they conveniently ignore the fact that it doesn’t even address the other five links. You often find such arguments under headings like “Christian Apologetics” or “Presuppositionists”.

Blaise Pascal took a different approach. He fell back on his formula for the Expected Value, which I discussed quite a bit in my three posts about playing the lottery. Here’s the logic which Pascal laid out.

Given the fact that (as we all know) believing in Jesus is what gets you into Heaven, and given the fact that Heaven is an infinite reward, and given the fact that the alternative is Hell, which is an infinite punishment, we can calculate the Expected Value for believing in Jesus. The formula will require some unknown quantities, but as you’ll see in a minute, their precise values don’t change the outcome. First, we need the probability that God exists. Let’s call that “g”. Like all probabilities, this is a number between zero and one. Because you can’t be 100% certain that God does not exist, that means g > 0. It might be 22% or 0.00000004% or it might be 0.000000000000000000001% but whatever it is, it’s not zero. Next, we need to ask the question what does it cost you to believe in a god that doesn’t exist. Let’s call this “c”. Pascal claimed that c was zero, but it still works if c is some other number, as long as c is finite.

EV for believing in Jesus = (g) x (infinite reward) –  (1-g) x (c)

Notice that, if g > 0 and c is finite, this result is always infinity, regardless of the specific values for c and g. Now consider the Expected Value for not believing in Jesus. For this calculation, we need one more number, the value of not believing in Jesus in a world where there is no god. Let’s call this “a”.

EV for not believing in Jesus = (1-g) x (a) – (g) x (infinite punishment)

Notice that, if g > 0 and a is finite, the result is always negative infinity.

Pascal’s conclusion from this is that, no matter how unlikely you think God’s existence might be, whether it’s 50% or 2% or 0.000000000000000001%, it doesn’t matter. When you multiply that probability times the infinite reward of going to Heaven, it’s always a safe bet for you to believe in Jesus.

There are so many flaws with this argument that there’s an entire page on Wikipedia devoted to explaining Pascal’s Wager and its flaws. I’m not going to try to repeat them all. I’ll just point out three which I thought of on my own.

Flaw #1: It uses circular logic.

The whole point of Pascal’s Wager is to try to decide if God exists and what you should do about it. The argument admits the possibility that God might not exist at all. Yet the argument is founded on the assumption that believing in Jesus gets you into Heaven and that Heaven is an infinite reward. If there is no god, then this assumption isn’t true at all. He started his proof for knowledge about God by assuming we have knowledge about God. That’s circular logic.

Flaw #2: It ignores alternatives (such as other religions).

Even if God does exist, that still wouldn’t prove that Heaven is real, or that Heaven is an infinite reward, or that believing in Jesus is what gets you into Heaven. Muslims believe that submission to the will of God is what gets you into Heaven, not belief in Jesus. Some religions believe that God has already decided whether you will get into Heaven or not and nothing you ever do has the power to change that decision. And Pascal conveniently ignored the possibility that there might be more than one god, and perhaps even different heavens. Then there’s one of my very favorite alternatives which I found on youtube: Keight’s Wager (“Keight” is pronounced like “eight”). Put yourself in God’s shoes for a minute. You’ve just created a universe. You’re lonely. You want to invite some people to join you in Heaven. What kind of people would you, God, want to hang out with? It’s easy to imagine that God is really into science. So maybe God would only invite into Heaven people who embrace the scientific method. Now, considering that there’s an amazing lack of evidence proving God’s existence, the only rational conclusion for a scientific-minded person to make is that God does not exist. Therefore, the perfect candidate for who God wants to invite into Heaven is…. an atheist! So, if you want the infinite reward of going to Heaven, your best strategy is to be an atheist. I’m not saying I actually believe Keight’s Wager. I’m just pointing out that Pascal’s Wager rests on unproven assumptions.

Flaw #3: The exact same logic leads to conclusions which are obviously wrong.

Suppose I show up at your door selling a bottle of water which came from the Fountain of Youth. Given the fact that (as we all know) drinking water from the Fountain of Youth bestows upon you the gift of immortality, and immortality is an infinite reward, let’s calculate the Expected Value for purchasing this bottle. We need the probability that I’m telling the truth about the water. Let’s call it “t”. You can’t be 100% sure that I’m lying, so t > 0. I didn’t specified the asking price for the bottle of water; let’s call it “p”.

EV = (t) x (infinite reward) – (1-t) x (p)

As long as p is a finite number and t is not zero, this formula always comes out to infinity. Therefore, you should definitely buy the bottle of water from me, no matter how much money I ask from you, and no matter how slim the chance is that I might be telling the truth. If the reward is infinite, then your only logical course of action is to hand over all your money.

Clearly, this is wrong-headed. Only a fool would hand over all their money to a stranger selling bottles of “magic” water. To suggest that logic demands that this must be the best course of action is just ridiculous.

.  .  .  .  .

Remember in my last post when I said that the Expected Value formula doesn’t work very well when you use very large numbers? Well, here’s a case where Pascal tried to apply the formula to INFINITE numbers, and it failed miserably. Frankly, he should have known better. But he was desperate. He knew deep down that he was 99.9% convinced that God doesn’t exist, but he badly wanted to keep clinging to some tiny scrap of hope. He couldn’t face the idea if giving up his belief. So he slapped together this appalling collection of bad logic and said he would keep on believing in Jesus anyway.

I can sympathize with Pascal’s situation. I struggled for years before I could finally give up my belief. After holding on to it for such a long time, it was very difficult to let go. I was a believer from childhood up until my early thirties.

I think that if I had started questioning my beliefs in my fifties or sixties, it would have been even harder to let go. I’m not sure if I would have been able to do it.

In conclusion… if you’re a believer who wants to try to bring me back into the light and you think to yourself “Hey! I know what to say to an Atheist. I’ll say what if you’re wrong? That’ll get him”… don’t even bother. I have spent way more time asking myself that very question than you ever will.


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