Pascal’s Wager

Blaise Pascal was a brilliant 17th century mathematician, physicist, and inventor.  He made enormous scientific and mathematical contributions from his teens, through his early 30s.  At age 31, following a religious conversion, he shifted much of his focus to religion and philosophy, becoming (unfortunately) somewhat less productive in mathematics and science in the process.  Pascal’s Wager appeared as just one of many essays within his Pensées (i.e. “thoughts”) publication.  Pascal’s wager is routinely used as an argument in one form or another (e.g. “You should believe, or you’ll be sorry!”) by Christians, though less so by professional apologists.  Pascal died at the young age of 39.

Blaise Pascal

The Text (from Blaise Pascal, Pensées, Section III, §233):

‘Who then will blame Christians for not being able to give a reason for their belief, since they profess a religion for which they cannot give a reason? They declare, in expounding it to the world, that it is a foolishness, stultitiam; and then you complain that they do not prove it! If they proved it, they would not keep their word; it is in lacking proofs, that they are not lacking in sense. “Yes, but although this excuses those who offer it as such, and takes away from them the blame of putting it forward without reason, it does not excuse those who receive it.” Let us then examine this point, and say, “God is, or He is not.” But to which side shall we incline? Reason can decide nothing here. There is an infinite chaos which separated us. A game is being played at the extremity of this infinite distance where heads or tails will turn up. What will you wager? According to reason, you can do neither the one thing nor the other; according to reason, you can defend neither of the propositions.

Do not then reprove for error those who have made a choice; for you know nothing about it. “No, but I blame them for having made, not this choice, but a choice; for again both he who chooses heads and he who chooses tails are equally at fault, they are both in the wrong. The true course is not to wager at all.”

Yes; but you must wager. It is not optional. You are embarked. Which will you choose then? Let us see. Since you must choose, let us see which interests you least. You have two things to lose, the true and the good; and two things to stake your reason and your will, your knowledge and your happiness; and your nature has two things to shun, error and misery. Your reason is no more shocked in choosing one rather than the other, since you must of necessity choose. This is one point settled. But your happiness? Let us weigh the gain and the loss in wagering that God is. Let us estimate these two chances. If you gain, you gain all; if you lose, you lose nothing. Wager, then, without hesitation that He is.—”That is very fine. Yes, I must wager; but I may perhaps wager too much.”—Let us see. Since there is an equal risk of gain and of loss, if you had only to gain two lives, instead of one, you might still wager. But if there were three lives to gain, you would have to play (since you are under the necessity of playing), and you would be imprudent, when you are forced to play, not to chance your life to gain three at a game where there is an equal risk of loss and gain. But there is an eternity of life and happiness. And this being so, if there were an infinity of chances, of which one only would be for you, you would still be right in wagering one to win two, and you would act stupidly, being obliged to play, by refusing to stake one life against three at a game in which out of an infinity of chances there is one for you, if there were an infinity of an infinitely happy life to gain. But there is here an infinity of an infinitely happy life to gain, a chance of gain against a finite number of chances of loss, and what you stake is finite. It is all divided; wherever the infinite is and there is not an infinity of chances of loss against that of gain, there is no time to hesitate, you must give all. And thus, when one is forced to play, he must renounce reason to preserve his life, rather than risk it for infinite gain, as likely to happen as the loss of nothingness.”

For it is no use to say it is uncertain if we will gain, and it is certain that we risk, and that the infinite distance between the certainty of what is staked and the uncertainty of what will be gained, equals the finite good which is certainly staked against the uncertain infinite. It is not so, as 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. There is not an infinite distance between the certainty staked and the uncertainty of the gain; that is untrue. In truth, there is an infinity between the certainty of gain and the certainty of loss. But the uncertainty of the gain is proportioned to the certainty of the stake according to the proportion of the chances of gain and loss. Hence it comes that, if there are as many risks on one side as on the other, the course is to play even; and then the certainty of the stake is equal to the uncertainty of the gain, so far is it from fact that there is an infinite distance between them. And so our proposition is of infinite force, when there is the finite to stake in a game where there are equal risks of gain and of loss, and the infinite to gain. This is demonstrable; and if men are capable of any truths, this is one.

“I confess it, I admit it. But, still, is there no means of seeing the faces of the cards?”—Yes, Scripture and the rest, etc. “Yes, but I have my hands tied and my mouth closed; I am forced to wager, and am not free. I am not released, and am so made that I cannot believe. What, then, would you have me do?”

True. But at least learn your inability to believe, since reason brings you to this, and yet you cannot believe. Endeavour then to convince yourself, not by increase of proofs of God, but by the abatement of your passions. You would like to attain faith, and do not know the way; you would like to cure yourself of unbelief, and ask the remedy for it. Learn of those who have been bound like you, and who now stake all their possessions. These are people who know the way which you would follow, and who are cured of an ill of which you would be cured. Follow the way by which they began; by acting as if they believed, taking the holy water, having masses said, etc. Even this will naturally make you believe, and deaden your acuteness.—”But this is what I am afraid of.”—And why? What have you to lose?

But to show you that this leads you there, it is this which will lessen the passions, which are your stumbling-blocks.

The end of this discourse.—Now, what harm will befall you in taking this side? You will be faithful, honest, humble, grateful, generous, a sincere friend, truthful. Certainly you will not have those poisonous pleasures, glory and luxury; but will you not have others? I will tell you that you will thereby gain in this life, and that, at each step you take on this road, you will see so great certainty of gain, so much nothingness in what you risk, that you will at last recognise that you have wagered for something certain and infinite, for which you have given nothing.

“Ah! This discourse transports me, charms me,” etc.

If this discourse pleases you and seems impressive, know that it is made by a man who has knelt, both before and after it, in prayer to that Being, infinite and without parts, before whom he lays all he has, for you also to lay before Him all you have for your own good and for His glory, that so strength may be given to lowliness.’[i]

The shorthand version boils down to:

  1. We can neither prove nor disprove God’s existence.
  2. A game is being played, and we’re in it whether we like it or not. We therefore have no choice but to wager on the existence or nonexistence of God.
  3. There are two (and only two) choices: Believe in God (specifically the Christian God), or don’t.
  4. The former choice brings an infinite reward (an eternal life of ultimate happiness), while costing nothing. If we’re wrong, we suffer the same fate (nothingness in Pascal’s view) as nonbelievers.
  5. Therefore, a risk-rewards evaluation says that the only sensible choice is to believe.
  6. If, we cannot just make ourselves sincerely believe, we should do the things believers do; in so doing, we will gradually come to believe.

The Rebuttal:

Point 1: Pascal got this mostly right.

  1. Theists have tried for millennia to prove the existence of their respective gods, and have come up empty.  Not only have they failed to prove the existence of their gods, they haven’t even come up with mildly compelling objective evidence.  While this doesn’t mean that god’s existence cannot be proven, we can at least conclude that (for now) god’s existence has not been proven.
  2. Claims by some atheists notwithstanding, it’s impossible to disprove the existence of god.  First, there is literally an infinite number of possible gods that one might hypothesize. Second, when one has a quiver containing an infinite number of supernatural arrows, one can defeat any rational argument. Every rational objection to the theology can always be met with more miracles, etc., or with the dismissive “The human mind can’t comprehend the mysteries of god.” While the rational person will quickly recognize the belief to be irrational, most believers seem to have a limitless capacity to rationalize the irrational.

Having said that, it may be possible to falsify (disprove) the existence of a given SPECIFIC god, if that god is sufficiently defined.  One can compare the claimed nature and actions of that god against objective evidence, to falsify the claims.  If I claimed that god is a 3 foot tall (corporeal and always visible) man named Morty, who lives at a specific address, it’s easy enough to verify whether such a man lives at that address.  If not, the claim is falsified.  However, if a 3 foot tall man named Morty DOES live there, we obviously haven’t proven anything as to whether he is, in fact, a god. Similarly, we CAN falsify at least some theist’s claims as to the nature of their god(s), based on the objective evidence.

Point 2: The claim (that we have no choice but to wager) is clearly false. Billions of people have lived and died without ever considering whether or not to believe in the Christian God. One could argue that by doing nothing, they implicitly placed their bets, but that position is inconsistent with Pascal’s language, in which he clearly says a conscious choice must be made.

Point 3: The claim that we have only two choices is a false dichotomy fallacy. We have far more options than just belief in the Christian god, or nonbelief. There are thousands of gods worshiped around the world, and a wide variety of nontheistic philosophies. So there are not two choices – there are thousands (at least).  This alone is enough to refute Pascal’s argument, since it invalidates the entire risk-rewards analysis.

Point 4: Pascal claimed that if the believer is wrong, he loses nothing.  This has multiple problems:

  1. He ignored the numerous other (non-Christian) religions that make equally extraordinary promises of rewards.
  2. He neglected the huge cost of being a believer, manifest in countless hours wasted studying the Bible, praying, etc., and money spent supporting false churches and preachers, More importantly, the believer is expected to make many decisions (including some of the most important decisions in life) based on the myths and superstitions of primitive men, rather than on reason and rationalism. And they spend far too much time and energy in pursuit of a nonexistent afterlife, rather than making the most of the one life that they know for sure that they have.
  3. Sadly, many believers are actually longing for an early end to this world (the ones that their children and grandchildren will inherit), rather than striving to leave the world a better place than they found it. 

Point 5: So based on his risk/rewards analysis, Pascal says we should choose to believe.  Aside from the already noted issues with the premises, His conclusion also has several problems:

  1. It suggests that we should just play the odds and choose to believe, out of what is essentially naked self-interest. If your god really does exist, and is all-knowing, one would expect that he would see through such a ploy.
  2. Many of the gods (including the Christian one) are reportedly “jealous gods”. So if I decide to choose one, and pick the wrong one, I may be worse off than choosing none, since I could just be pissing off the one true god.
  3. Even Christians can’t agree on what it takes to be saved. Some say it’s predestined. Some say it’s through faith. Some say it’s through love. Some say it’s through our deeds. Some say you have to be baptized in just the right way. Some say you have to accept Jesus. Some say you must have the Holy Spirit. Some say you must belong to their particular denomination…. So according to many millions of believers, belief alone isn’t enough.

Point 6: Pascal suggests that for one who has trouble believing, they should go through the motions, and eventually, they’ll believe.  Speaking as a former believer, I can say that going through the motions did nothing to overcome the cognitive dissonance caused by practicing a religion that no longer made rational sense to me.  And I’m clearly not alone.

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