# Pascal's Wager **URL:** \ **Category:** Great Debates\ **Created:** [March 6, 2000, 10:37pm UTC](https://boards.straightdope.com/t/pascals-wager/17746 "2000-03-06T22:37:00Z")\ **Posts on this page:** 20\ **Page:** 3
**Author:** ![Gilligan](https://avatars.discourse-cdn.com/v4/letter/g/e0b2c6/32.png) [@Gilligan](https://boards.straightdope.com/u/Gilligan)\ **Post date:** [March 8, 2000, 7:48pm UTC](https://boards.straightdope.com/t/pascals-wager/17746/41 "2000-03-08T19:48:00Z")
Thank you for the phrase “if it even makes sense to speak of _choosing what to believe_”, Spiritus. My belief is that in fact it doesn’t make sense (naturally, I didn’t choose this belief). Thus I think this is where the wager fails. The question of whether or not we should take the bet, by believing in God, presupposes that this is a choice we make. This choice is not “free” or “not free” or “somewhat free”, it is “non-existent”. Beeruser, interesting lottery analogy, but of course people play the “cold” number strategy, too, when it comes to the numbers. Maybe they should pick the least popular belief. ---
**Author:** ![Liberal](https://avatars.discourse-cdn.com/v4/letter/l/848f3c/32.png) [@Liberal](https://boards.straightdope.com/u/Liberal)\ **Post date:** [March 8, 2000, 9:23pm UTC](https://boards.straightdope.com/t/pascals-wager/17746/42 "2000-03-08T21:23:00Z")
As noted previously, the existence of arguments against Pascal’s Wager absolutely **does not** constitute a refutation of it. An argument is simply that: an argument. Pascal makes an argument and Rescher makes an argument. The second argument is not assumed a priori to refute the first. A refuation occurs **when an argument is proved false**. And, as I noted, Rescher and others, _even after posing arguments to counter Pascal_, still accept the validity of his Wager. It is disingenuous of sites that list these arguments against the Wager and represent them as refutations. Here is a reputable site, the[Stanford Encyclopedia of Philosophy](http://setis.library.usyd.edu.au/stanford/entries/pascal-wager/). From it, I quote: > [@](#): > > A number of authors who have been otherwise critical of the Wager **have explicitly conceded that the Wager is valid** —e.g. Mackie 1982, Rescher 1985, Mougin and Sober 1994, and most emphatically, Hacking 1972. That is, these authors **agree with Pascal** that wagering for God really is rationally mandated by Pascal’s decision matrix in tandem with positive probability for God’s existence, and the decision theoretic account of rational action. It is true, as you can see there, that _some_ writers have dismissed the Wager, but the alleged **refutation** of it is an urban legend. I hope that by this weekend, I’ll find time to address and counter the arguments against the Wager that I posted. (Oh, Lord, that sounded an awful lot like you know whom!) 😉 ---
**Author:** ![CalifBoomer](https://avatars.discourse-cdn.com/v4/letter/c/f1d935/32.png) [@CalifBoomer](https://boards.straightdope.com/u/CalifBoomer)\ **Post date:** [March 9, 2000, 2:36am UTC](https://boards.straightdope.com/t/pascals-wager/17746/43 "2000-03-09T02:36:00Z")
slythe: > [@](#): > > Or are you trying to say that yet another unproven entity (The Holy Ghost) can be > used to help prove the existance of your god? WOW! Your mind is already made up, isn’t it? God (as I understand God), is an infinite being. We are _finite_ beings. By definition we cannot understand or even prove or disprove the existence of God. (if we could understand/prove/disprove God, that God would not be big enough). Whatever intellect/reason/logic we bring to this message board is still limited. It does help, however, to have somewhat of an open mind when discussing perhaps unknowable issues with these limitations. There most assuredly are forces at work in this universe that we are not aware of, much less comprehend. ---
**Author:** ![Czarcasm](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/czarcasm/32/4050_2.png) [@Czarcasm](https://boards.straightdope.com/u/Czarcasm)\ **Post date:** [March 9, 2000, 3:44am UTC](https://boards.straightdope.com/t/pascals-wager/17746/44 "2000-03-09T03:44:00Z")
Calif, in _my_ world, if something cannot be seen, felt, measured, or understood, it doesn’t exist. You can believe in nothing if you want to, but I’ve got better things to do. ---
**Author:** ![CalifBoomer](https://avatars.discourse-cdn.com/v4/letter/c/f1d935/32.png) [@CalifBoomer](https://boards.straightdope.com/u/CalifBoomer)\ **Post date:** [March 9, 2000, 3:49am UTC](https://boards.straightdope.com/t/pascals-wager/17746/45 "2000-03-09T03:49:00Z")
slythe: You deny the existence of anything your limited faculties can percieve? So, if you were in an accident, or had a brain aneurysm, and slipped into a coma, the world around would no longer exist, even though it was still a reality for billions of others? ---
**Author:** ![jab1](https://avatars.discourse-cdn.com/v4/letter/j/ee7513/32.png) [@jab1](https://boards.straightdope.com/u/jab1)\ **Post date:** [March 9, 2000, 4:03am UTC](https://boards.straightdope.com/t/pascals-wager/17746/46 "2000-03-09T04:03:00Z")
A hypothetical situation: You are a fan of _The Wizard of Oz_. You like the book so much, you join a fan club. You have discussions, you have parties, you even have bake sales and such to raise money for charity, you discuss the meanings of various passages and what was the book really about, anyway? (“Baum was telling us not go off the silver standard?” _Not true._) You discuss the many movies (“No one actually committed suicide on the movie set, you know.” “Oliver Hardy played the Tin Man in one silent version.” _Both true._) and TV specials and other Oz books, including those written by other authors. (Science fiction author Philip Jose Farmer wrote _A Barnstormer in Oz_, the adventures of Dorothy’s full-grown aviator son, Hank.) The other fans seem like a nice bunch, but a few seem to take it way too seriously. _Way_ too seriously. In fact, some of them think the book _is a true story_. They, in fact, think Oz is really Heaven itself. That Glinda summoned Dorothy, being brave and true in spirit, to assist her in geting rid of the Wicked Witch of the West, that Dorothy’s trip, therefore, was not an accident. And now, Oz is a paradise awaiting all of us, but ONLY if you belieive it is true. “This is ridiculous,” you scoff. But they seem so sincere. And there are so many of them. They can’t ALL be deluded, can they? And what if they’re right? “What if OZ is Heaven and I’ll miss out if I don’t believe? And all they want me to do is attend a meeting once a week and contribute a little cash to keep it all going. It seems like such a small investment of time and money. And if I’m wrong, I’ve lost little.” Oh, really? Substitute Heaven’s Gate for the Holy Church of the Blessed Dorothy and you can see where it could lead. Substitute Scientology for HCBD and see which is really more absurd. (Click [here](http://www.xenu.com/archive/leaflet/xemuleaf.htm) to see what’s at the core of Scientology. It’s actually MORE absurd than my fictional Church of Dorothy.) Substitute ANY religion, IMHO. Just what are you really risking, anyway? Maybe it’s your ability to distinguish fact from fantasy. Maybe it’s your sanity. Maybe it’s your very life. * * * When all else fails, ask Cecil. ---
**Author:** ![Czarcasm](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/czarcasm/32/4050_2.png) [@Czarcasm](https://boards.straightdope.com/u/Czarcasm)\ **Post date:** [March 9, 2000, 4:23am UTC](https://boards.straightdope.com/t/pascals-wager/17746/47 "2000-03-09T04:23:00Z")
Silly, silly Calif. Your argument was that “God” cannot be seen or measured, _not_ that I couldn’t see him. If he cannot be seen, heard, felt, measured, or understood in any way, we are beyond what _I_ may or may not be able to sense, now arn’t we? If I were in a coma, and the outside world was not visible or measurable in any way to anybody, then for all intents and purposes, it does not exist. Like your Zeus. I mean Odin. I mean Santa Claus. I mean God. It’s hard to tell all these fairy tales apart sometimes, y’know. 🙂 ---
**Author:** ![SingleDad](https://avatars.discourse-cdn.com/v4/letter/s/9e8a1a/32.png) [@SingleDad](https://boards.straightdope.com/u/SingleDad)\ **Post date:** [March 9, 2000, 6:49am UTC](https://boards.straightdope.com/t/pascals-wager/17746/48 "2000-03-09T06:49:00Z")
Pascal’s wager expressed in semi-mathematical notation (subscripts are denoted by braces). I assign the values because I’m assuming that Pascal considers his wager valid at any non-zero probability of God’s existence, and asserts (by implication) that the belief has neither cost nor intrinsic reward in mundane reality (“if you lose, you lose nothing”). Therefore: 1. p{God} = 1/infinity _The probability of God’s existence is infitesimal but greater than zero._ 2. r{belief} = infinite _The reward of belief in God is infinite._ 3. c{belief} = 0 _The cost of belief in God is zero._ 4. r{disbelief} = 0 _The reward of disbelief is zero._ 5. c{disbelief} = 0 _The cost of disbelief is zero._ Therefore the payoffs come to: 1. q(belief) = (p{God} \* r{belief}) - ((1 - p{God}) \* c{belief}) _the probability-weighted payoff of belief_ 2. q(disbelief) = (p{God} \* c{disbelief}) - ((1 - (p{God}) \* r(disbelief)) Therefore, Pascal asserts that: 1. q(belief) \> q(disbelief) Thus, by subsitution: 1. (p{God} \* r{belief}) - ((1 - p{God}) \* c{belief}) \> (p{God} \* c{disbelief}) - ((1 - (p{God}) \* r(disbelief)) and further: 1. (1/infinity \* infinity) - ((1 - 1/infinity) \* 0) \> (1/infinity \* 0) - ((1 - 1/infinity) \* 0) Now probability is not generally applicable to infinite quantities, but we’ll give him the benefit of the doubt and allow that (infinity \* 1/infinity) has some unspecified value greater than zero, noted as **Q**. Therefore: Q - 0 \> 0 - 0 and thus Q \> 0 Q.E.D. BUT! Pascal has included a **faulty premise** : The cost of belief is _not_ zero! The cost of belief has a measurable value: the difference between my ‘natural’ will and the that which my belief, accepted through only the evidece of the Wager. This cost is not only nonzero, but it’s not infitesimal. Thus we have to replace premise (4) with 1. c(belief) = x _The cost of belief is some numerically meaningful nonzero quantity_ Therefore, the proper expression of the wager is: 1. (1/infinity \* infinity) - ((1 - 1/infinity) \* x) \> (1/infinity \* 0) - ((1 - 1/infinity) \* 0) Since (1 - 1/infinity) ~ 1, Q - (1 \* x) \> 0 and thus Q \> x Since Q does not have a definite value and x does, the conclusion that Q \> x cannot be proven and thus fails to prove the wager. To make Pascal’s Wager a true statement you must assert that **belief costs nothing** , which trivializes the nature of belief. By this analysis, Lib, I make my claim that Pascal’s Wager is conclusively refuted. Note that if you assign a non-zero value to the cost of disbelief, you contradict a premise of the wager that, “if you lose, you lose nothing”. * * * He’s the sort to stand on a hilltop in a thunderstorm wearing wet copper armor, shouting ‘All Gods are Bastards!’ ---
**Author:** ![SingleDad](https://avatars.discourse-cdn.com/v4/letter/s/9e8a1a/32.png) [@SingleDad](https://boards.straightdope.com/u/SingleDad)\ **Post date:** [March 9, 2000, 7:30am UTC](https://boards.straightdope.com/t/pascals-wager/17746/49 "2000-03-09T07:30:00Z")
After reading Mr. Hájek’s analysis more carefully, I discern a few more ways in which Pascal makes unwarranted assumptions in his wager. I must assign a non-infinitesimle probability to his existence. Under this stipulation, the wager fails unless you can give me an objective method whereby I might assign such a numerical probability. I must assign an infinite value to the reward of belief yet, I must assign a zero value to the reward of disbelief. If you rig the game this way, you can get someone to profess any belief you want. For instance, I might wager you $1,000,000 against $0 that the Goddard Middle School Jr. Varsity football team can defeat the Green Bay Packers in a game of NFL regulation football. I can extend the payoff, and reduce the probability (e.g. staking a trillion dollars on the US Army vs. a dozen trained rats) without changing the nature of the wager. Regardless, of how you estimate their chances, you have to take Goddard (or the rats). Therefore I have ‘proven’ that you believe that Goddard is superior to the Packers. But really, Pascal says it all when he states, “Reason can decide nothing here.” He is a religious man, musing on his own religious decision. He isn’t offering a rational means of deciding whether to believe or not. ---
**Author:** ![SingleDad](https://avatars.discourse-cdn.com/v4/letter/s/9e8a1a/32.png) [@SingleDad](https://boards.straightdope.com/u/SingleDad)\ **Post date:** [March 9, 2000, 7:32am UTC](https://boards.straightdope.com/t/pascals-wager/17746/50 "2000-03-09T07:32:00Z")
Ugh, I have to stop posting after midnight or I make too many errors in, punctuation and speling. Sorry. ---
**Author:** ![JoeyBlades](https://avatars.discourse-cdn.com/v4/letter/j/a87d85/32.png) [@JoeyBlades](https://boards.straightdope.com/u/JoeyBlades)\ **Post date:** [March 9, 2000, 2:51pm UTC](https://boards.straightdope.com/t/pascals-wager/17746/51 "2000-03-09T14:51:00Z")
Spiritus, You wrote: > [@](#): > > Your opinion on this matter is not universal. It is not even universal among Christians. It is not even universal among Christian sects derived from Protestantism. I will not refute these statements. Many people have claimed to know the mind of God. This may lead them to invent requirements based on their personal assessments. I don’t pretend to know the mind of God, nor do I even know the mind of men who “know the mind of God”. I do know a little about what the scriptures have to say on the subject, specifically scriptures recounting the words of the man I believe to be the son of God and therefore the most reliable source on the Mind of God. I’m pretty sure he never said that God’s promise of everlasting life required that you go to church on Sunday, give money to the church, give up drinking, give up golf, or make any other lifestyle changes. True, many Christians do make lifestyle changes, but it’s not a requirement. > [@](#): > > As you so correctly point out, faith _will_ change the way one views other issues and it _will_ change the way one lives one’s life. Thus, the choice of faith (if it even makes sense to speak of _choosing what to believe_) is not “free”. The change in behavior is not a consequence of faith, it’s another choice the faithful often make. It’s a separate decision. Here’s a really bad analogy… If I go to dinner at a nice resturant and really enjoy the meal and the service, I’m likely to leave a nice tip. The tip is not a required cost, it’s a voluntary cost and based on a completely separate decision process. ---
**Author:** ![JoeyBlades](https://avatars.discourse-cdn.com/v4/letter/j/a87d85/32.png) [@JoeyBlades](https://boards.straightdope.com/u/JoeyBlades)\ **Post date:** [March 9, 2000, 3:01pm UTC](https://boards.straightdope.com/t/pascals-wager/17746/52 "2000-03-09T15:01:00Z")
SingleDad, You wrote: > [@](#): > > 1. c{disbelief} = 0 > The cost of disbelief is zero. I’m confused. Wouldn’t Pascal say the cost of disbelief is non zero and negative? If you wager that God does not exist and find to your dismay in the afterlife that God does exist, there’s a huge penalty. ---
**Author:** ![StrTrkr777](https://avatars.discourse-cdn.com/v4/letter/s/fbc32d/32.png) [@StrTrkr777](https://boards.straightdope.com/u/StrTrkr777)\ **Post date:** [March 9, 2000, 3:19pm UTC](https://boards.straightdope.com/t/pascals-wager/17746/53 "2000-03-09T15:19:00Z")
Just out of curiosity, Slythe, why do you get involved in these posts? Obviously it is your perrogative to read and post whatever you like, but it seems that there must be a reason to post. My personal reason is that I wish to try and answer anyone’s honest questions about God or the Bible. I do not claim to know everything about God or the Bible, but I have studied both for many years. I realize that many people have had run-ins with Churches and Christians who did not live nor act in a Christ-like manner. I also, seek to show others that these people are not the norm, that in fact there are folks (several on this board) who are good Christians who do honestly try to live as Christ taught. Jeffery ---
**Author:** ![jab1](https://avatars.discourse-cdn.com/v4/letter/j/ee7513/32.png) [@jab1](https://boards.straightdope.com/u/jab1)\ **Post date:** [March 9, 2000, 9:04pm UTC](https://boards.straightdope.com/t/pascals-wager/17746/54 "2000-03-09T21:04:00Z")
I have a question for **StrTrkr777**. You chose your UserName because you are a _Star Trek_ fan, right? You’ve even said you’re one on that thread I started on why it was better than _Star Wars_. Question: Are you aware that the creator of _Trek_, Gene Roddenberry, was an atheist? Isn’t it a contradiction for a Christian to be a fan of anything created by an atheist? Roddenberry’s atheism did not come through very strongly on _The Original Series_ because NBC didn’t want to alienate any believers. His skepticism was much more evident in the syndicated _Next Generation_, however. * * * When all else fails, ask Cecil. ---
**Author:** ![SingleDad](https://avatars.discourse-cdn.com/v4/letter/s/9e8a1a/32.png) [@SingleDad](https://boards.straightdope.com/u/SingleDad)\ **Post date:** [March 9, 2000, 9:11pm UTC](https://boards.straightdope.com/t/pascals-wager/17746/55 "2000-03-09T21:11:00Z")
> [@](#): > > I’m confused. Wouldn’t Pascal say the cost of disbelief is non zero and negative? If you wager that God does not exist and find to your dismay in the afterlife that God does exist, there’s a huge penalty. Pascal’s _Wager_ does not posit punishment for disbelief, just lack of access to the reward. I’m analyzing the wager, not Pascal’s personal beliefs or Christian theology. ---
**Author:** ![JoeyBlades](https://avatars.discourse-cdn.com/v4/letter/j/a87d85/32.png) [@JoeyBlades](https://boards.straightdope.com/u/JoeyBlades)\ **Post date:** [March 9, 2000, 11:03pm UTC](https://boards.straightdope.com/t/pascals-wager/17746/56 "2000-03-09T23:03:00Z")
jab1 asks: > [@](#): > > Isn’t it a contradiction for a Christian to be a fan of anything created by an atheist? It would be a very limited world indeed for Christians if this were so… Good Christians don’t judge others for their beliefs and they certainly don’t judge art by the beliefs of the artists. This doesn’t mean that Christians might not find some expressions of art offensive to their religous beliefs, but this is normally a content bias. Do atheists refuse to appreciate anything created by a Christian? ---
**Author:** ![Wendolynne](https://avatars.discourse-cdn.com/v4/letter/w/848f3c/32.png) [@Wendolynne](https://boards.straightdope.com/u/Wendolynne)\ **Post date:** [March 10, 2000, 2:25am UTC](https://boards.straightdope.com/t/pascals-wager/17746/57 "2000-03-10T02:25:00Z")
You Christians who cannot even imagine the contrapositive are in grave danger of being a sheep in your next incarnation. Seriously. Or maybe an ox. You were given a magnificent brain in this incarnation, but you failed to use it to its greatest potential, and are likely to slide back on the evolutionary scale next time around. And it doesn’t matter if you believe it or not. Whether you choose to believe has no bearing on the outcome. ---
**Author:** ![Little\_Nemo](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/little_nemo/32/3120_2.png) [@Little\_Nemo](https://boards.straightdope.com/u/Little_Nemo)\ **Post date:** [March 10, 2000, 5:59am UTC](https://boards.straightdope.com/t/pascals-wager/17746/58 "2000-03-10T05:59:00Z")
SingleDad, I want to praise you on your post. I attempted to make the same points but your mathematical proof was much clearer. The only thing I’d add to it would be to point out there is no reason to assume r{belief} = infinite is true (I realize Pascal made this assumption). R{belief} could equal _minus_ infinite; ie there exists the possibility that belief in the wrong God will produce a greater punishment than atheism. With this factor q(belief) can be less than q(non-belief) even if c{belief} = 0. On a seperate issue, several people seem to be making a distinction between belief and practice. There appear to be arguments that belief alone does not require any change in a person’s actions and therefore costs nothing. I’d contradict this by pointing out that even a mental declaration of belief is an action in the sense of this issue. Otherwise you could have a practising Christian who follows all of the outward rituals of his faith but secretly says in his head “There is no God but Allah and Mohamed is his prophet.” After all, he could then argue that his belief in Allah cost him nothing because it didn’t change his practice as a Christian; it’s just a little extra insurance in case it turns out he picked the wrong religion. But I think most Christians would agree that a Christian God would not favor a person who only maintained an outward show of being a Christian while inwardly believing as a Muslim. ---
**Author:** ![CalifBoomer](https://avatars.discourse-cdn.com/v4/letter/c/f1d935/32.png) [@CalifBoomer](https://boards.straightdope.com/u/CalifBoomer)\ **Post date:** [March 10, 2000, 6:05am UTC](https://boards.straightdope.com/t/pascals-wager/17746/59 "2000-03-10T06:05:00Z")
jab 1: > [@](#): > > Isn’t it a contradiction for a Christian to be a fan of anything created by an atheist? But it’s ok for a Darwin sycophant to quote scripture? Smacks of hypocrisy, jab… ---
**Author:** ![CalifBoomer](https://avatars.discourse-cdn.com/v4/letter/c/f1d935/32.png) [@CalifBoomer](https://boards.straightdope.com/u/CalifBoomer)\ **Post date:** [March 10, 2000, 6:09am UTC](https://boards.straightdope.com/t/pascals-wager/17746/60 "2000-03-10T06:09:00Z")
Single Dad: > [@](#): > > Pascal’s Wager does not posit punishment for disbelief, just lack of access to the > reward. Why do you assume they are mutually exclusive? [Previous page](https://boards.straightdope.com/t/pascals-wager/17746.md?page=2) [Next page](https://boards.straightdope.com/t/pascals-wager/17746.md?page=4)