Pascal's Wager

by Brian 27. August 2009 07:09

An atheist coworker once boasted he wrote a paper in school successfully refuting Pascal’s Wager as a proof of God’s existence. At the time it seemed like a strange thing to brag about. I later learned the Wager is primarily considered a pragmatic argument for believing in God rather than an ontological proof. It is often cited by theists and nontheists alike and is certainly one of the most famous arguments in the philosophy of religion. But mere “belief” in God is hardly adequate, as even the demons believe. (James 2:19) So what is Pascal’s Wager and how useful is it in Christian apologetics?

The Wager comes from the Pensées, Blaise Pascal’s unfinished written work of his thoughts. The most relevant translated text follows[1]:

"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... 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... But your happiness? Let us weigh the gain and the loss in wagering that God is... If you gain, you gain all; if you lose, you lose nothing. Wager, then, without hesitation that He is."

Considered alongside his other writings, it is not exactly clear what Pascal meant by “reason can decide nothing here.” Even though Pascal disdained philosophical arguments for God’s existence, he embraced Christian evidences, such as evidence for Christ’s resurrection[2]. Nevertheless, the Wager argument stands on its own and is commonly expressed in the following payoff matrix:

  1. I believe in God
    1. God exists = maximal gain
    2. God does not exist = minimal loss
  2. I do not believe in God
    1. God exists = maximal loss
    2. God does not exist = minimal gain

According to decision theory, rationality requires you perform the action of maximum expected utility. Utility is computed by multiplying the mutually exclusive outcomes by the subjective probability of each of the two states’ obtaining and adding the values together. Taking an agnostic position; let us assume for the moment the probability God exists is 0.5 and assign somewhat conservative values[3] of maximal=100 (payoff/penalty if God exists) and minimal =1 (payoff/penalty if God does not exist)…

In the case of “I believe in God”:
(100 * 0.5) + (-1 * 0.5) = 45.5

In the case of “I do not believe in God”
(-100 * 0.5) + (1 * 0.5) = -45.5

It is clear from the above example that “believing” has a better payoff than “not believing.” And note the payoff for believing over not believing increases proportionally with the difference between maximal and minimal outcome values - assuming payoff and penalty are at equal and opposites ends. Sometimes the Wager is expressed using infinite outcome value in place of maximal due to the eternal nature of either states obtaining. This drives the payoff to infinite positive and negative utility leaving you with a no-brainer. But then infinite values raise issues in standard decision theory and can be avoided by instead selecting arbitrarily large finite values.

Common Objections
  1. The subjective utilities vary from person to person: This is illustrated by the attitude, “I wouldn’t be happy in heaven with all of those harp players anyway.” In other words, if Heaven is not appealing and Hell does not sound too bad, then the resulting payoff/penalties are not as divergent. If you also believe the existence of God has a low probability, then the payoff might even be greater if you choose not believe. However, assuming you are not much better off in Heaven than in Hell is a baseless and reckless assumption. From a Christian perspective; Heaven is eternal joy in the presence of God and Hell is eternal separation from God where there will be “weeping and gnashing of teeth.” (Luke 13:28) The disparity between minimal and maximal is more likely to be unfathomably great if Heaven and Hell exist. If you are going to take the Wager seriously then it would be wise to err on the side of caution and assume the disparity in outcome between Heaven and Hell is great. 
  2. Low probability God exists: Nontheists who believe the probability God exists is very low (near zero) will claim the payoff for believing isn’t very compelling. Although the subjective outcome values for maximal and minimal swamp[4] out low probability for all but the hardened atheist, it is true the Wager’s force is weakened by low probability. The argument is clearly more compelling to the honest agnostic. 
  3. Zero probability that God exists: The proposition “God does not exist” is not a self-evident brute fact with absolute certainty. Hence zero probability is not a valid objection. 
  4. The many-gods objection: This is based on the idea that there is a plurality of deities to choose from and where only one choice is likely to be true. This creates a disjunction between Christianity, Islamism, Judaism, Mormonism, etc. If Allah is the true God instead of the Christian God, then choosing to believe as a Christian is practically equivalent to choosing not to believe. In other words, the “God does not exist” column is subdivided into multiple wrong-choice columns. However, in a decision-theoretic context, we are justified in ignoring states which have a remotely small probability of obtaining[5]. In other words, given my background knowledge, I can reasonably reject Odin, Zeus and Shiva and limit my choices to a small number of live options. Given a limited number of plausible choices, the outcome values again swamp the payoff, compelling one to make a choice to believe – even if it is potentially the wrong choice.

A Christian Perspective
The standard payoff matrix does not reflect the Christian perspective. To begin with, mere belief in the existence of God does not result in a maximal gain. It is a relationship with God through Jesus Christ that matters. Furthermore, the idea the Christian potentially suffers a minimal loss in this life while the unbeliever enjoys minimal gain is backward in the general sense. As one who has been on both sides of the fence, I can attest to the fact the Christian life in the here and now has more to offer than the life of the unbeliever. Although I personally find it more demanding, it is also more rewarding. In light of this, the standard payoff matrix could be revised as follows:

  1. I accept Jesus Christ as Savior
    1. God raised Jesus from the dead = maximal gain
    2. Jesus did not rise from the dead = minimal gain
  2. I reject Jesus Christ as Savior
    1. God raised Jesus from the dead = maximal loss
    2. Jesus did not rise from the dead = minimal loss

According to this revised version, it seems obvious which route results in maximum utility. Unfortunately, there is a slight problem with this argument given the many-gods objection I mentioned. If God did not raise Jesus from the dead, then the Christian potentially suffers maximal loss given another ultimate reality obtains. For example, Allah sends me to Hell for believing in Jesus would result in a maximal loss, not minimal gain. The Bible comes at this from another angle within the context of the Law: (i.e. Judaic Law) “And if Christ has not been raised, your faith is futile; you are still in your sins. 18Then those also who have fallen asleep in Christ are lost. 19If only for this life we have hope in Christ, we are to be pitied more than all men.” (1 Corinthians 15:17-19 NIV) On the other hand, if you have narrowed down your live options to Christianity and atheism, then the revised matrix is sound and the pragmatic force of the argument remains strong.

The Bottom Line
Yet having shown greater utility obtained by believing in anything seems to have very little effect on most of us. Upon first hearing of Pascal’s Wager, I must admit I was unmoved. It may have pragmatic force, but it lacks epistemic force. Even given a valuable payoff, how successful have you been in forcing yourself to believe in anything solely based on the reward? What if I agreed to give you $1,000,000 to believe there are ruins of an ancient civilization on Mars where our NASA probe is about to land (which has some minimal plausibility) and a kick in the shin if you are wrong. Decision theory might dictate in this case you should believe. Yet it is obvious, utility alone cannot form an honest belief. As C. S. Lewis wrote: “If Christianity is untrue, then no honest man will want to believe it, however helpful it might be: if it is true, every honest man will want to believe it, even if it gives him no help at all.” There simply is no direct path from utility to honest belief. But do not lose heart; it seems Pascal’s Wager remains relevant to the Christian apologist. Although it is unlikely to convince a nontheist to submit his or her will to God, it ought to compel an honest agnostic to delve deeper into eternal matters and consider sources leading to maximum utility. Therefore,

The Wager should provide great impetus for the honest agnostic to seek out the Truth. The honest agnostic is equally committed to the belief in proposition P (God exists) and ~P (God does not exist.) However, many agnostics typically live their lives like atheists. They may claim no prevailing belief either way due to a variety of reasons; lack of knowledge or concern, doubt, etc., but their lives are lived as if God does not exist. So in effect, the agnostic has already chosen the route of minimal utility. Upon reflection, the Wager should awaken the conscious and pique the interest of the honest agnostic. After all, if you are galloping down the road to Hell wearing horse blinders, the Wager should compel you to take them off and look around a bit. Of course, some agnostics have already considered these matters and remain unconvinced.

Nevertheless, we should not strive to believe in the option of minimal utility. The simple truth is; theists and nontheists alike function to some degree on faith. No worldview is without epistemic tension. I know from personal experience anyone who claims to be an atheist with absolute certainty in their position is being dishonest – either openly or to themselves. The Christian is in the same boat. I have great certainty and confidence in my faith when I am so moved by the Holy Spirit. Other times my faith perseveres with a degree of tension. Given the reality of epistemic tension in all substantive worldview, it is not uncommon for us to pursue those things strengthening our belief and avoid those which undermine it. The authors we prefer are often the ones we agree with. The arguments carrying the most weight are often the ones reinforcing our view of things. Even though honest investigation requires one consider alternate sources and viewpoints, the Wager argument suggests we ought not to prefer sources leading to the minimal utility. So if you have already read Hume and Dawkins, now is a good time to pick up a Bible.

[1] 1910 Trotter translation

[2] Philosophical Foundations for a Christian Worldview, Moreland, Craig, 2003, pg. 160

[3] The outcome values here have only relational meaning: In the case of maximal=100 and minimal=1, you are 100 times better off (however measured) if the maximal outcome obtains

[4] Overwhelming magnitude X, such that the resultant is primarily derived from X

[5] Ibid

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About the author

I am a Christian, husband, father of two daughters, an owner of ISC, lead architect of MapDotNet, armchair apologist and philosopher, writer of hand-crafted electronic music, and a kid around anything that flies (rockets, planes, copters, boomerangs, hot air baloons, lawn furniture)

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