Course Notes — Blaise Pascal, “The Wager”

by Daniel A. Kaufman

https://www.york.ac.uk/depts/maths/histstat/pascal_wager.pdf

The students in my Introduction to Philosophy course just took their second exam, which covers material from Montaigne, Pascal, and Descartes.  From Montaigne we read two essays, “Of Pedantry” and “Of the Education of Children,” and from Descartes, we read the Meditations on First Philosophy.  Both have been a regular part of my introductory syllabus for several years now.

The Pascal material is a new addition and replaces St. Anselm’s Monologion — which students had difficulty digesting – so it is the first time I have taught it at Missouri State.  “The Wager” is short, written in an accessible style and fascinating, not to mention tremendously influential.  Indeed, there is an entire entry devoted to it in the Stanford Encyclopedia of Philosophy.

One of the interesting things about the Wager is that its argument takes a very different form from its medieval predecessors.  Where the Scholastics tried to demonstrate that God exists by way logical proofs, Pascal maintained that one should believe in God, because doing so is one’s best bet.  The Wager is remarkable, then, in that it suggests that belief in God, even in the absence of any evidence or reasons for thinking he exists, is the rational choice.

Pascal observes that either God exists or he doesn’t and that one can either believe in him or not, and then imagines the consequences of belief or non-belief, given God’s existence or non-existence.  The result is a rational-decision scenario, described by the following table:

 

God Exists

 

God Does Not Exist
 

Believe in God

 

Enjoy eternal paradise.

 

Nothing lost.

 

Don’t believe in God

 

Suffer eternal damnation.

 

Nothing lost.

Pascal maintains that the rational choice is clearly belief, given that it yields the best range of outcomes – eternal paradise or nothing lost – while unbelief yields the worst range of outcomes – eternal damnation or nothing lost.  And on first glance, it certainly looks as if he is right.

In class, I try to strike a delicate balance.  On the one hand, I prefer not to hide from students what I think.  For one thing, when one does this, it simply invites students to speculate as to what one’s views are, which means that they will often get them wrong.  For another, the students are adults to whom one should be able to speak without the sort of self-censorship and mild dissembling that are appropriate when speaking with children.  On the other hand, I don’t want to tell students what they should think about philosophical questions, for which there are always a number of reasonable points of view.  So, rather than characterize the Wager as demonstrably fallacious – which I think it is – I chose instead to describe three things about it that should give a person pause and encourage further consideration.

First, I am quite skeptical of the claim that when one believes in God, when in fact there is none, nothing is lost.   Depending on the commitments that come with such a belief – strict dietary laws, severe constraints on sexual behavior, limitations on what one can do on the Sabbath, etc. – quite a lot may be lost.  If I was to commit to Orthodox Jewish belief, I would never be able to eat some of my favorite foods, for the entirety of my life.  I wouldn’t just consider that a loss, but a substantial one.

Second, the Wager depends on a very specific religious commitment to Christianity or other religions that involve eternal reward and punishment for belief/non-belief, which is by no means all of them – Judaism, for example, has no conception of eternal punishment for non-belief.  And if one imagines a very different kind of God – say a philosopher-God who prefers honest skeptics to hedge-betting believers – the relevant risks and rewards are actually inverted.  The point just is that there is nothing in the Wager itself that legitimates the belief in any particular God or religious tradition, and yet, one must assume very particular ones for the good and bad bets to work out the way Pascal wants them to.

Finally, the Wager fallaciously infers probabilities from the logical principle of bivalence.  It is true that logically speaking God either exists or doesn’t, but it doesn’t follow from this that God’s existence is a 50/50 matter.  But, the Wager only works in the way Pascal wants it to, if the chances of God’s existence is an even split.  If the chances of God existing are one in ten million, then the idea that it is reasonable to give up so many of life’s greatest joys on such a slim likelihood is hard to sustain.  And beyond this, I’m dubious that something like God’s existence can even be assigned a probability at all.  After all, what would the basis of such an assignment be?

The Wager is interesting and challenging for any reader, but for my students, who overwhelmingly come from evangelical and Pentecostal backgrounds, it is of special interest and is especially thought-provoking.  They were interested throughout the discussion, and participated to a greater degree than they have with respect to almost any other subject we’ve taken up thus far.

15 Comments »

  1. Agree with the first and second objections against Pascal’s wager

    But with regards to the third objection, couldn’t one maintain that regardless of the probability of God’s existence, the expected value (eternal life in paradise) of believing in Him greatly outweighs the expected value of not doing so (eternal damnation)?

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  2. Saw the below passage in the Stanford encyclopedia entry:

    “Pascal’s guiding insight is that the argument from expectation goes through equally well whatever your probability for God’s existence is, provided that it is non-zero and finite (non-infinitesimal)—‘a chance of gain against a finite number of chances of loss’.[4]”

    I think this suggests that the only skew of probabilities possible to override the expected value is if the probability of God’s existence is infinitely small… which doesn’t seem plausible to me personally.

    Don’t mean to belabor the point but I think for me the above was the key insight of Pascal’s wager, though Pascal muddles this by giving it a probability of half, as explained in the footnote accompanying the paragraph above in the Stanford entry.

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    • Yeah I don’t agree with the entry on this point. Of course what counts as reasonable is somewhat subjective, so I would never present it as any kind of knock down argument.

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  3. On this one the same objections you raised popped up for me very quickly before reading further to where you raise them. I suppose I must have given Pascals’ argument some thought years ago.

    I do think it raises interesting questions. One might be are there conditions when it sometimes make sense to believe in something that cannot be proved false? Another might concern the nature of belief, how it develops, and whether or not we can convince ourselves into belief based on logic or rationality.

    I have been on a bit of an Iris Murdock reading spree delving into why she considers herself a platonist ( ‘The Sovierngty of the Good’, & her philosophical writings). If I remember correctly Dan, you admire her novels more so than her philosophical ideas. I wanted to read someone sympathetic to this type of belief since it is not my orientation, and am finding her work very interesting so far.

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  4. I first came across Pascal’s Wager when I was a teenager. I thought it was an interesting argument, though I wasn’t entirely sure that it was a legitimate use of probability. At that time, I considered myself an evangelical Christian. So I was glad that the argument supported the view that I held. But since I did not need to be persuaded, it is hard to judge how persuasive the argument was.

    A few years later, when I was withdrawing from religion, I remembered the argument. And, somehow, it had no persuasive power at all.

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  5. I think this suggests that the only skew of probabilities possible to override the expected value is if the probability of God’s existence is infinitely small… which doesn’t seem plausible to me personally.

    The probability of God’s existence is all that relevant here. The argument is about the probability of the entire Christian package, taken as a whole.

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  6. God exists but he doesn’t care about the planet earth.
    God exists and he’s sending everyone to hell because – why not?
    God does not exist, but the Afterlife Superman does, and he assures us all of bliss- at least until his own demise in 5 billion years.

    God exists but there is no afterlife.
    Gods exist, but which of them has the road-map to Tralfamadore?
    God does not exist, but the road-map to Tralfamadore can be found under a rock in Chicago. I know where it is. Anyone getting to Tralfamadore gets to live for 7 aeons with 7 celestial virgins (but they must remain virgins – no touching or you end up in hell.

    It actually took some years before I realized that the Wager hinges on acceptance of the *Christian* mythos as standard by which to determine a “50/50” chance between choices. And without that 50/50 choice, it just doesn’t work.

    Pascal was a mathematician, and his work contributed to the development of what would become known as probability theory. So I can only attribute this reduction to 50/50 chance choices to his faith. He *needed* his faith to be rational, rather than trusting his rationalism to lead to a faith (which would have looked like Spinoza or at least the deism that was becoming popular among intellectuals of the day.

    I admit that there is no rational argument against theistic faith, which ioriginates largely as an emotional response to the world. But there is no rational argument for god’s existence.

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  7. I should explain the possibilities I remarked in my previous comment: The point being that “god” as an empty signifier – that is as a sign capable of being loaded with an indefinite number of possible significations – cannot properly ground nor be assigned a proper probability value. Therefore, no wager can be placed; or rather, every wager will be forfeit, not by being lost, but by never reaching resolution.

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  8. I happened to be reading the “Travel Letters of Lady Mary Wortley Montagu”. In a letter dated 1717 she is discussing the Albanians, called by her the “Arnaut”:

    “But of all the religions I have seen, the Arnaut seems to me the most particular. They are natives of Arnaoutlich, the ancient Macedonia, and still retain something of the courage and hardiness, though they have lost the name, of Macedonians, being the best militia in the Turkish empire, and the only check upon the janissaries. They are foot soldiers; we had a guard of them, relieved in every considerable town we passed: they are all clothed and armed at their own expense, generally lusty young fellows, dressed in clean white coarse cloth, carrying guns of a prodigious length, which they run with on their shoulders as if they did not feel the weight of them, the leader singing a sort of rude tune, not unpleasant, and the rest making up the chorus. These people, living between Christians and Mahometans, and not being skilled in controversy, declare that they are utterly unable to judge which religion is best; but, to be certain of not entirely rejecting the truth, they very prudently follow both and go to the mosques on Fridays and the church on Sundays, saying for their excuse, that at the day of judgement they are sure of protection from the true prophet; but which that is, they are not able to determine in this world. I believe there is no other race of mankind have so modest an opinion of their own capacity.”

    I guess they were true Pascalians.

    Alan

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  9. Professor Kaufman: I, for one, would like to hear your take on “Of Pedantry” and “Of the Education of Children.”

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