Pascal's Wager
Between Prudence and Truth
This is the first of three essays revisiting Pascal’s famous Wager from a twenty-first-century perspective. Some of the conclusions will be challenging to some readers. I have tried to balance clarity, completeness, and brevity—not always successfully. The overall arc of the third essay ties back to a conclusion that I think is not obvious to all readers. We are examining ideas that are almost half a millennium old. They are still relevant in today’s world.
Near the end of his life, Blaise Pascal (d. 1662) wrote an argument in defense of religious belief. He believed that everyone would have to take this wager. The Wager was published after his death in 1670, in a collection of his notes called Pensées ("Thoughts"). It remains important in popular Christian apologetics to this day.
It’s especially popular on social media; I have seen at least half a dozen (usually mangled) versions of it in my social media feeds in the past few months. Here is one example I saw on Facebook:
It is better to follow the teachings of Jesus and treat people undeservedly kindly and find out there is no God, than to do otherwise and have to answer to Him. Jesus was dying to have a relationship with you so He did. [sic]
For many believers, arguments like this stand as a prudent justification for religious faith.
There are always obvious issues with memeified social media posts, but there are also serious issues with Pascal’s Wager itself. The most significant of these is this: If we properly consider the Wager against the world that exists, it fails spectacularly.
Rather than a logical justification for religious belief, it becomes a logical proof that any specific religious belief—no matter how strong the convictions of the believer—is almost certainly wrong. Depending on a few factors, the precise probabilities can vary by a few orders of magnitude in some framings, but, for all practical purposes, very closely approach zero.
Pascal’s Wager, still invoked by many Christians as justification for belief and action, is actually an argument that any specific religious belief is wrong.
This matters. A lot.
It matters if integrity matters. It matters if truth is important. It matters in a world shredding itself into tatters.
The Wager
First, let’s get the wager right. The original framing is in archaic French. A good English translation is here.
Allow me to paraphrase the argument. If you want to take issue with my work, this is the first place I could get it wrong.
God either exists or does not exist.
We cannot use reason to decide if God does or does not exist. The question is beyond reason.
“You must wager. It is not optional.”
If God actually exists, and you bet that He does, you win eternal happiness in heaven.
This is an infinitely good payoff.
If God does exist and you bet that He does not, you end up with eternal punishment.
This is an infinitely bad payoff.
If God does not exist, then your wager is essentially irrelevant; the payoffs are finite (not infinite), so they will be swamped in the final calculation1.
The expected value of the wager is equal to the sum of the products of the probabilities of each scenario and the value of their payoffs2.
If the payoffs are infinite, the probabilities do not matter. Even a vanishingly small probability that God exists makes the value of the “believe” scenario infinitely larger than the “don’t believe.”
The “believe” scenario dominates in every case unless you can conclusively prove that the probability that God exists is zero. Pascal himself stated, “Reason can decide nothing here”, and I think this point stands without argument—it would be foolhardy to believe that p(God Exists)=0.
Therefore, one must believe.
Pascal acknowledged that some people couldn’t believe in God. His advice was (again to paraphrase), “try really hard to believe. Until you can make yourself believe, at least go through the motions so it looks like you do. Maybe acting like you believe will make it easier to believe.”
He also claimed that the price of belief was essentially zero—certainly offset by the eternal rewards for getting it right. Any costs were minimal and finite. What have you to lose, in the face of a God who will condemn you to eternal punishment if you choose not to believe?
I’ll have some thoughts about both of those later.
Pascal himself noted that this was not a bet designed to get to truth, and this is a point often missed.
In other words, it’s not an ontological argument (an argument about what is). It is a prudential argument to justify action.
It is about what one ought to do—an admittedly self-serving plan to achieve eternal reward under a simple scheme where one either believed the right thing or spent an eternity burning in hell.
This, in a nutshell, is Pascal’s Wager.
So, Who Is This Guy?
This is not an idea to be lightly discarded. Pascal was a towering intellect. Frankly, I think of my own intellect as a candle beside his as a raging bonfire.
He was far ahead of his contemporaries in many fields at once. He essentially invented probability theory and created decision models without which our society would collapse. (The Wager is early work on that.) His work and correspondence with Fermat laid the groundwork for modern actuarial science and the insurance business.
He solved practical engineering problems and his work on fluid dynamics led to modern hydraulics. He built the first commercially-produced mechanical calculator and was an acknowledged mathematical genius at age 16. He made major contributions that Leibniz would later expand into calculus. Footnotes to his life might also mention that he invented public transit.
On a personal note, he was a thinker who shaped my own mind as a young man. I struggled with his writing, both philosophically and logically, and realized that some of it was beyond my grasp. Regardless, I became a better person and a much better thinker for the effort. I cannot convey to you the respect I have—and I think anyone must have—for this man and his work.
So, I’m certainly not disparaging Pascal or his Wager. (Though I will happily disparage weak apologetics, no matter how passionate. And these seem to dominate much of the social media space and in many of our churches.)
Here’s the point—this was one of the smartest guys who ever lived. Our society owes a lot to him and his work. When an intellect of this caliber makes such a glaring logical error as we find in the Wager, it points to something else at work.
That’s why I’m writing this.
In my next post, we will look at exactly how Pascal was wrong, and why it matters.
This was Pascal’s move, but it’s worth noting that other thinkers have noted that infinite (or even overwhelmingly large or small) payoffs can essentially break expected value comparisons. This may more properly belong as a critique, but if we are willing to let the infinities stand, it should be considered up front.
To restate for clarity, if the mathematical language is unclear: for each scenario, you multiply the probability of the payoff times the value of the payoff and then you add them all up.