[Note: I had hoped to be able to post my thoughts on the GodBlogCon for today but got sidetracked while working on other projects (a short article about the conference for World magazine and prepping for an interview for BBC Radio). Having already recycled material for over a week, I beg your indulgence for one more day. Regular blogging will resume on Tuesday.]
Life is a gamble. Every day we are forced to make decisions based on imperfect knowledge, unsure of the outcomes of our choices. We do the best we can with what we have available, developing strategies based on experience, accumulated information, and calculations of probabilities. Traveling to Seattle in April? We pack an umbrella since its likely to rain. Meeting a co-worker for lunch? No reason to rush since she is never on time.
Almost every rational decision we make in life is a based on what we assume to be the expected outcome. We make our choices in order to maximize our gains and minimize our losses, attempting all the while to to boost our expected value of every specific outcome. In order to better understand this process, it might be useful to examine this decision-making process from a hypothetical example.
Let’s assume that you have just finished eating your favorite snack, a chocolate brownie, when you realize that you have nothing to drink. I notice your predicament and kindly offer you a glass of milk but warn that I had put arsenic in the drink. Although we’re only acquaintances you know the following information about me: I’m psychotic, I have access to arsenic, and that I tell the truth 67% of the time. While you’re extremely thirsty and tempted to drink the milk, you aren’t quite ready to die yet. What should you do?
In order to determine the most rational choice, you have to determine the expected value for each outcome. The expected value (EV) would be the probability of an outcome multiplied by the payoff less the costs of that choice: EV = (Probability x Payoff) – Cost.
Based on my propensity to make honest claims, you assume the probability of the milk being poisoned to be 67%. The payoff -- the benefit of drinking the milk – is a bit more difficult to determine. Let’s assume that you gain no other pleasure in life other than eating brownies and washing them down with milk. We can measure this pleasure in units of “brownies and milk” (BM) and use that as our basis for a payoff. Drinking this glass of milk would provide you with 1 BM of pleasure while the cost would be the outcome if the milk is poisoned.
For this example we’ll pretend that you are a 50 year old male who enjoys this snack once a day. Based on a life expectancy of 72 years, you can expect to have 8,030 BMs of pleasure in your lifetime (22 years x 365 days x 1 BM). Plugged into this formula we get the following two outcomes:
Assuming the milk is poisoned -- (67% x 1BM) – 8030 BM = - 8029.33
Assuming the milk is not poisoned -- (33% x 1BM) – 0BM = .33
Since the cost of drinking the milk far outweighs any pleasure you might receive, the rational choice would be avoid the milk (and to stay as far away from me as possible).
There is, however, a 37% chance that the milk is not poisoned. In the short term you could get lucky and “beat the odds”, receiving 1 BM of pleasure from the drink. But if the example were repeated you would, more often than not, end up with a serious stomachache before falling over dead. A rational gambler, therefore, would always refuse the milk.
The French mathematician and philosopher Blaise Pascal claimed that we are making a similar bet when it comes to God. By the way in which live our lives we are either betting that there is a God or that there is not. Since there are no third options, we are either making the decision either ignorant default or by rational choice.
Like Stephen Unwin, Pascal believed that there is no overwhelming evidence that can remove all doubt about which choice we should decide. Practical reason may help us determine which is more probable but it cannot ultimately decide the matter one way or the other. What we can do, according to Pascal, is make a rational gamble.
For the sake of argument, let’s assume (as Pascal does) that the evidence will lead us to choose between Christian theism and atheism.* Each choice will result in different expected values based on the unique payoffs and costs.
In order to determine the costs, let’s make the distinctions as clear as possible for our rational gambler by bringing in a cruel dictator to compel him to make his choice. The tyrant not only forces the gambler to bet but vows that if he selects Christianity he will be instantly martyred. If he bets on atheism, however, he will have a life of ease and pleasure – a daily ration of brownies and milk.
To quantify this choice, let’s assume that one unit of pleasure (BM again) is derived for every day of life that is lived. If the 50-year-old rational gambler chooses Christianity, he will lose 8,030 units of pleasure. In contrast, by choosing atheism, he will incur no cost at all. The cost part of the equation can be framed as C = 8,030 BMs and A = 0 BM.
But what about the payoff? What does the rational gambler gain if his bet on Christianity turns out to be the right one? While we cannot know all the details, we know that the belief entails the promise of everlasting life and eternal joy. However we choose to quantify this benefit, the payoff would be infinite. The atheist’s payoff would be limited to the finite benefits that he would receive in the remainder of his life, a figure we calculated at 8,030 BMs.
Now let’s plug these figures into our formula to determine the expected value of each choice.
Christianity: (50% x Infinite) – 8,030 BMs = Infinite BM
Atheism: (50% x 8,030 BM) – 0 BM = 4015 BM
Obviously, the rational gambler would be wise to bet on Christianity. In fact, even if we were to reduce the probability of Christian theism being true to .000001%, he would still end up with a better expected value than he would by betting on atheism.
Pascal’s argument differs from my example in many respects but the point is still the same: practical reason should lead us to act as if Christian theism is true. But we can’t just act as if something were true that we don’t really believe, can we? As Pascal answered his rhetorical objector:
"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?
Such an argument is unlikely to persuade someone who is already convinced that atheism is true. For those who have rejected or refused to objectively examine the evidence for Christian theism, living as if the belief were true simply to test its veracity is hardly a compelling option. Pascal, who believed that the passions rather than reason were the root of every denial of God, was most likely aware of this when he proposed the wager. The strength of the argument, however, lies not in its ability to convince but in what it removes. Pascal’s wager essentially removes any appeals to practical reason that the atheist might have been tempted to fall back on and shows that when forced to make the rational gamble on God, the atheist chooses the most irrational choice.
(Sources: Blaise Pascal, Penses; Thomas V. Morris, Making Sense of It All)
*Obviously, Christian theism is not the only possibility since any theistic belief that entailed a God and an afterlife of eternal, blissful existence would also fit into this framework. For now, though, I’ll set aside any claims of a false dilemma and save explanations for why Christianity is the best of all possible theistic choices for another time.
See also: Wagering a Life: Urwin and the Probability of God
Update: Jeremy Pierce left a relevant comment in the last version that bears repeating:
As for the argument that this is belief for the wrong reasons, that's a fair point, but Pascal's response to the problem of involuntary belief (quoted by Joe in the post) gives the resources to respond to this also. It's not belief for the right reasons, because it's not belief at all. It's putting yourself in a position so that if God really exists you'll form the right beliefs for the right reasons. Pascal has given reasons to put yourself in that position by seeking out God, engaging in a community of faith for the sake of seeing if there's something to it, being involved with its practices such as prayer, scripture reading, and public worship. It's a reason to investigate, but investigation can't be a mere intellectual exercise or it won't be investigating the right sort of thing.
1
I can understand you need some time to write and article, but to prep for a radio interview? It's not like you have to make sure your tie is straight. Since it's for the BBC, you'll want to remember that most of the Brits are nothing but amazed at the huge number of Americans who attend Sunday services and look at us with a cocked eyebrow when they read about the movement here to inject Intelligent Design in the classroom and religion into politics.
posted on 10.17.2005 12:21 PM2
I can tell you don't "gamble" much because a "true gambler" would just forsake the glass of milk and drink right from the "jug" knowing Mr. psychotic wouldn't waste his arsenic on the whole enchilada.
posted on 10.17.2005 12:37 PM
3
AndyS,
I can understand you need some time to write and article, but to prep for a radio interview?
According to my boss (whose from the UK), BBC Radio Five is very fast paced and the speakers talk at a clip of 170 words per minute. Being from Texas I speak a bit slower -- about half that speed -- so I have to prep by talking like a New Yorker. ; )
posted on 10.17.2005 1:00 PM4
I am so thankful for the perspective you brought at the GodBlogCon. I wish I'd gotten time to tell you personally. Thank you for what you are doing and for setting such an example for so many of us.
God bless,
Lores Rizkalla
Just A Woman
www.justawoman.org
5
The biggest problem with this sort of reasoning involves assigning probabilities to states that are emprically incalculable. In this context, 50% is as arbitrary as 0.000001% or any other number. It is not logically sound to simply split the difference, nor is it rhetorically generous to reduce the likelihood of your own favored state being true to some negligible number. Basically the whole exercise is bogus.
A much more logically sound defense of Christianity would be based on faith, and may include some combination of culture and personal preference and choice. For example: "I was born into a Christian household and raised among Christian traditions. As I grew into an adult capable of reasoned, independent thought, I reevaluated the belief system I was raised in, compared it to the alternatives, and concluded that I prefer being a Christian. Based on this preference, I choose to exercise faith in the factual claims of Christianity, including the existence of God, the plan of salvation, and the fate of the human soul after death."
Such a rationale holds two advantages over Pascal's Wager: First, it is not logically ridiculous. Second, it divorces belief from empiricism, thereby inocculating the believer against any assault on faith that is founded on empricism.
posted on 10.17.2005 3:02 PM6
My favorite line of the whole article . . . "Based on a life expectancy of 72 years, you can expect to have 8,030 BMs of pleasure in your lifetime . . . "
posted on 10.17.2005 3:22 PM7
And both are brown...
This is why economists measure happiness in utils, still perhaps an unfortunate-sounding term but not as funny.
More seriously, I agree with Zarathustra that this apologetic misses the point. Adding numbers to Pascal's wager misses the point of the wager even. The part you quoted at the bottom about having masses said, etc. - in evangelical terms, to reference Luther, putting yourself in the place where faith is possible - is the real point. People often abstract the wager from the rest of the Pensees, which it should be remembered, is an unfinished work. But even in that part of it that we have, we can discern a wider structure in which Pascal is striving to make his intended audience, pleasure seekers who distract themselves with temporary goods, aware of their true state of helplessness and uncertainty in an infinite universe absent revelation (except that mediated by the Church, which they reject).
For the wager to work, Pascal's audience must have already been prepared by his earlier sections to arrive at a point where they don't know what the odds of God's existence vs. non-existence are. Assigning values of relative happiness is the opposite of what they can do, because, as mentioned by the previous commentor, such numbers are completely arbitrary. However, Pascal hopes that his readers will see that the certainty with which life in the Church will provide them is an adequate substitute for the life of pleasure, which he has (in a Boethian sort of move) revealed to be transitory. They can for a while fake faith, and Pascal's belief in the efficacy of the Catholic sacramental system gives him confidence that God will bring them into a true faith if they keep doing the right thing long enough.
It should be remembered that Pascal was a devout Catholic (with Jansenist sympathies) and lived in a context where Catholicism or religious indifference were the only real options, at least in his opinion. Thus, there wasn't a false dilemma, as there is in modern applications of the wager. Furthermore, the wager works much better for people who believe, as he did, in the innate effectuality of the sacraments. All he had to do was get people to start going to confession, in a sense. Evangelical apologists have to do a lot more.
8
Joe,
Being from Texas I speak a bit slower ...
Hey, let them hear that Texas drawl. Europeans are in love with the Southwest. Of course, a reminder that some of us are still upset about the Brits burning down the Whitehouse in the War of 1812 is also in order. And that royalty thing... When will they get over it?
posted on 10.17.2005 3:50 PM9
I've always liked Pascal's wager, but I do have a problem with your formulation - if you approach it from only a rewards scenario, I believe that I would actually make the opposite wager - that I would wager for atheism rather than Christianity. Consider the following scenario:
You are on a game show and have already won a car (a modest reward). The host offers you the opportunity to trade the car for what is behind the curtain. There could be one of two things behind the curtain - pleasures beyond your wildest dreams, or a firing squad that will kill you instantly. In that caes, which would you take? I'd take the car, thank you very much. The reason is that though the magnitudes of the two possible rewards are vastly different, they are both of the same kind - a reward. However, the other option, the firing squad, is of a different kind entirely - an infinite punishment -the cessation of life into nonexistence.
To apply it to the formulation of Pascal's wager that you stated, if I choose Christianity and suffer instant martyrdom, if it is not true I have experienced an infinite punishment - the loss of the only life I have to live. However, if I embrace atheism, and am wrong, I have extended my life at least a few more moments. Are not those few more moments, even if less glorious than the reward of heaven, infinitely preferable to instant nonexistence?
The formulations of Pascal's Wager that I have seen depend much less on the possible rewards of heaven and much more on the potential eternal, infinite loss of hell, which I believe is a much stronger form of the argument. In that formulation, the threat of eternal suffering is even greater than the threat of nonexistence.
Interestingly, as a result it seems that without a real threat of hell in theology one takes the teeth out of Pascal's wager.
posted on 10.17.2005 4:04 PM10
Sorry, the first sentence of the third paragraph should read ". . .if I choose Christianity and suffer instant martyrdom AND AM WRONG. . ."
posted on 10.17.2005 4:17 PM11
I pretty much agree with MyThoughts is saying. This is essentially a logic exercise to demonstrate the point being made in the ridiculous bumper sticker which reads " If you don't believe in god, you'd better be right".
To do any sort of weighted logic assesment of any particular choice, you need to be able to weight the outcomes objectively using proven empirical evidence. As MyThoughts points out, the notion that only a non-Christian faces the threat of hell is by definition unprovable and certainly can't be weighted with any objective measure.
A more accurate way to look at that situation would be to say that the Atheist looks at religion and concludes that the "weighted value" of a Christian lifestyle is impossible to determine. It could provide anywhere from -infinity BMs (the threat that Christinaity could actually lead to an enternity of suffering) to +infinity BMs with no real evidence to conclude which is the more probable outcome. One would reasonably conclude that a weighted average of all of the possible outcomes in that scenario should be zero. In that case an Athiest lifestyle becomes the obvious logical upper hand.
This brings me to my point. It's not that Athiests fail to understand the consequences of their non belief, if in fact they are wrong. If they believed that there was even the slimmest of chances that Christian faith was telling the truth, the decision making process would be ridiculously simple. Athiests believe it is impossible to assess the consequence becasue there is no possible way to observe the outcome.
12
Fun. A gambling themed post at TEO. I haven't gotten all the way though, but first:
EV = (Probability x Payoff) – Cost
is close, but more accurately:
EV = (Probability of successful outcome x payoff) + (probability of negative outcome x cost)
For example, if i was to bet you on a coin flip, and pay you $2 for heads, but you pay $1 only if its tails:
EV = (1/2)(2) + (1/2)(-1)
hence, your EV is $.50 per flip.
posted on 10.18.2005 3:16 PM13
Betting and gambling. Thats not very evangelical is it?, or have the goal posts been moved... again?
posted on 10.18.2005 3:31 PM14
BMs? This is something of which an objective measure can be made. What one person derives as pleasure from not living a Christian life, may be another's despair. Personally, I obtain joy from living a life seeking Christ. Others may not, what is good for me may not be good for everybody. It sure seems rational to me that would be good for everybody, but, heh, everybody's entitled to live their own lives.
posted on 10.18.2005 3:36 PM15
"Betting and gambling. Thats not very evangelical is it?, or have the goal posts been moved... again?"
A lot of gambling is about understanding statistics applied to games. Whether you like to place money bets or not, understanding odds and game theory and such things can relevant to many aspects of life.
But, heh, there's no reason you can't get along fine in life without it. Some of us are just a little more decionmakingly-challenged,I guess.
posted on 10.18.2005 3:42 PM16
oops. Meant to say--This is NOT something of which an objective measure can be made.
17
Who believes in clouds and harps? I think something about wine and virgins is actually in the Qu'ran (correct me if I'm wrong), whereas all it says in the Bible is about a golden city, the restoration of creation to an Edenic state, kings of the earth bringing in their treasures, and Christ dwelling physically with His people. While some of those things (esp. the first) are metaphorical, I believe, at least to some extent, that's a far different picture than the cloud and harp image, which I'd like to see the real origin of sometime.
posted on 10.18.2005 6:07 PM18
The big problem with this is WHICH god you should believe in. Almost every modern god (at least in monotheism, a pretty modern development as far as gods go) is a jealous god, and demands strict adherence to specific dictates in order to get your infinite reward. Usually there is infinite suffering associated with choosing wrongly. You can't just cherrypick an infinite reward with your preferred god and assume that every other claim is false, because by and large they are using the same reasoning and evidence (or lack thereof) to back up a very similar but conflicting claim.
From where I sit it all looks like a lose-lose proposition. Assuming you buy into gods at all, since if you don't you can simply enjoy the very real rewards in the life you have.
posted on 10.19.2005 12:22 PM19
Addressed this (Jeff S.'s concern) in my comment. In original context (17th-century Catholic France), Pascal saw religious indifferent and Catholicism as the only viable options. Hence, no false dilemma. But, I agree, today that's not the case.
posted on 10.19.2005 11:10 PM20
Such an argument is unlikely to persuade someone who is already convinced that atheism is true.
This idea is omnipresent among believers, and one supposes that it brings the devout a measure of contentment; it suggests that atheism is a choice, equivalent to religious belief and constituting in itself a belief system. This is terribly incorrect, and it is one of the primary fallacies of Pascal's Wager.
In reality (while there may be particular exceptions), the atheist* should be viewed as a "non-believer," i.e., one who tries to hold no views that are unsupportable. Yes, the rational atheist rejects the notion of gods and magic, heavens and hells, sins and saints, but the rationalist also dismisses tooth fairies, Santa Clauses, UFOs, and other claims of the supernatural. All such beliefs are considered to be foolishness and not credible.
Atheism is not, thus, "anti-Christian," rather it is "anti-nonrational." Think of it like this: Were I to tell you that I have a tiny magic wizard named "Bob" in my pocket, a little guy who sees all, knows all, and can make anything imaginable happen, you would probably request proof. "Take him out and let's look at him," you'd say.
A reasonable request. So I tell you no, that he's invisible, and can't be seen, or touched, or anything and that you just have to take it on faith that he exists - oh, and he wrote a little book you can read, so there's your proof - you'd tell me to take a hike. Now, the key idea is that whereas I'm a Bob-Believer, your refusal to join me is not equivalent to my position. You simply dismiss me out of hand because my claims are patently absurd.
See the difference?
posted on 10.23.2005 10:18 AM