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Pascal’s Wager

The French mathematician Blaise Pascal (1623-1662) is rightly remembered as one of the true geniuses of his day—and indeed of the modern era.  He made important intellectual contributions to an immense array of subject ranging from probability theory and calculation (having invented a mechanical calculator at the age of 19) to physics and the study of fluids and vacuums to public transportation and religion.  One of Pascal’s most enduring contributions before dying at the relatively young age of 39 is his argument concerning whether to believe in God’s existence, which he outlines in his book Pensées (lit., Thoughts), from which the following passage is drawn.  Here, Pascal represents a rather pessimistic view toward natural theology as such, and hence toward reason’s capacity to support faith in God.  Instead, when it comes to the decision of whether to believe or not believe, Pascal contends that we must place a bet of sorts, bearing in mind the heavenly (or hellish) stakes involved.  This argument is most commonly known simply as Pascal’s Wager.

Text: Blaise Pascal’s “Wager” from Pensées.

Learning Outcomes:

  • Evaluate the logic and assumptions underlying Pascal's decision-theoretic approach to religious belief. What would we call this in the business world?  
  • Analyze the relationship between authentic belief and strategic reasoning.
  • Apply Pascal's Wager framework to contemporary decision-making scenarios involving uncertainty. 

Consider: Do you think that Pascal’s approach is more helpful or more harmful to the life of faith? 

 

Text:

  Blaise Pascal’s “Wager” from Pensées

Infinite, nothing.—The soul of man is cast into the body, in which it finds number, time, dimension; it reasons thereon, and calls this nature or necessity, and cannot believe aught else.

Unity joined to infinity increases it not, any more than a foot measure added to infinite space. The finite is annihilated in presence of the infinite and becomes simply nought. Thus our intellect before God, thus our justice before the divine justice. There is not so great a disproportion between our justice and that of God, as between unity and infinity.

The justice of God must be as vast as his mercy, but justice towards the reprobate is less vast, and should be less amazing than mercy towards the elect.

We know that there is an infinite, but are ignorant of its nature. As we know it to be false that numbers are finite, it must therefore be true that there is an infinity in number, but what this is we know not. It can neither be odd nor even, for the addition of an unit can make no change in the nature of number; yet it is a number, and every number is either odd or even, at least this is understood of every finite number.

Thus we may well know that there is a God, without knowing what he is.

We know then the existence and the nature of the finite, because we also are finite and have dimension.

We know the existence of the infinite, and are ignorant of its nature, because it has dimension like us, but not limits like us. But we know neither the existence nor the nature of God, because he has neither dimension nor limits.

But by faith we know his existence, by glory we shall know his nature. Now I have already shown that we can know well the existence of a thing without knowing its nature.

Let us now speak according to the light of nature.

If there be a God, he is infinitely incomprehensible, since having neither parts nor limits he has no relation to us. We are then incapable of knowing either what he is or if he is. This being so, who will dare to undertake the solution of the question? Not we, who have no relation to him.

Who then will blame Christians for not being able to give a reason for their faith; those who profess a religion for which they cannot give a reason? They declare in putting it forth to the world that it is a foolishness, stultitiam, and then you complain that they do not prove it. Were they to prove it they would not keep their word, it is in lacking proof 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 forth 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 determine nothing about it. There is an infinite gulf fixed between us. A game is playing at the extremity of this infinite distance in which heads or tails may turn up. What will you wager? There is no reason for backing either one or the other, you cannot reasonably argue in favour of either.

Do not then accuse of error those who have already chosen, for you know nothing about it.—No, but I blame them for having made, not this choice, but a choice, for again both the man who calls ‘heads’ and his adversary are equally to blame, they are both in the wrong; the true course is not to wager at all.—

Yes, but you must wager; this depends not on your will, you are embarked in the affair. Which will you choose? Let us see. Since you must choose, let us see which least interests you. You have two things to lose, truth and good, and two things to stake, your reason and your will, your knowledge and your happiness; and your nature has two things to avoid, error and misery. Since you must needs choose, your reason is no more wounded in choosing one than the other. Here is one point cleared up, but what of your happiness? Let us weigh the gain and the loss in choosing heads that God is. Let us weigh the two cases: if you gain, you gain all; if you lose, you lose nothing. Wager then unhesitatingly that he is.—You are right. Yes, I must wager, but I may stake too much.—Let us see. Since there is an equal chance of gain and loss, if you had only to gain two lives for one, you might still wager. But were there three of them to gain, you would have to play, since needs must that you play, and you would be imprudent, since you must play, not to chance your life to gain three at a game where the chances of loss or gain are even. But there is an eternity of life and happiness. And that being so, were there an infinity of chances of which one only would be for you, you would still be right to stake one to win two, and you would act foolishly, being obliged to play, did you refuse to stake one life against three at a game in which out of an infinity of chances there be one for you, if there were an infinity of an infinitely happy life to win. But there is here an infinity of an infinitely happy life to win, a chance of gain against a finite number of chances of loss, and what you stake is finite; that is decided. Wherever the infinite exists and there is not an infinity of chances of loss against that of gain, there is no room for hesitation, you must risk the whole. Thus when a man is forced to play he must renounce reason to keep life, rather than hazard it for infinite gain, which is as likely to happen as the loss of nothingness.

For it is of no avail to say it is uncertain that we gain, and certain that we risk, and that the infinite distance between the certainty of that which is staked and the uncertainty of what we shall gain, equals the finite good which is certainly staked against an uncertain infinite. This is not so. Every gambler stakes a certainty to gain an uncertainty, and yet he stakes a finite certainty against a finite uncertainty without acting unreasonably. It is false to say there is infinite distance between the certain stake and the uncertain gain. There is in truth an infinity between the certainty of gain and the certainty of loss. But the uncertainty of gain is proportioned to the certainty of the stake, according to the proportion of chances of gain and loss, and if therefore there are as many chances on one side as on the other, the game is even. And thus the certainty of the venture is equal to the uncertainty of the winnings, so far is it from the truth that there is infinite distance between them. So that our argument is of infinite force, if we stake the finite in a game where there are equal chances of gain and loss, and the infinite is the winnings. This is demonstrable, and if men are capable of any truths, this is one.