Wednesday, November 26, 2008

The Problem with Pascal's Wager

The genius of Blaise Pascal no one doubts.  The man has had attributed to him a law, a triangle, and a wager.  Yes, there is a Pascal's Law (a unit of measurement of pressure is named after him as well), a Pascal's Triangle (remember geometry?), and Pascal's Wager.  I will be focusing on the latter one, however.  Pascal's Wager is a way of showing that, despite the fact that reason cannot explain the existence of God, one ought still to believe in God.  Essentially, it is a more complex version of a rather simplistic argument we've all probably encountered.  If someone were trying to convince you to believe in God, they might say something to the effect of: "Well, what good is not believing?  You might as well believe."  This is the same type of thinking of Pascal, although I'm positive Blaise put much more thought into his argument.  

What it boils down to is this:  IF you were to wager (I'll show why this is important later) on the existence of God, then one should always wager that God exists.  The basis of this is that God either exists or doesn't exist.  You can either wager that he exists or wager that he doesn't exist.  IF you wager that God exists, and he does, there is an infinite gain, and just a finite loss -- the finite loss being perhaps giving up on some things because of religious beliefs during life, while the infinite gain, we're assuming, would be heaven or some sort of afterlife.  IF you wager that God exists, and he does not, there is a finite loss and nothing is gained.  The finite loss again being the luxuries and other things you gave up during your life time, and of course you gained nothing in the end for your self-restriction.    

Now, IF you wager that God does not exist, and God does exist, then there is an infinite loss and only a finite gain, where the finite gain is the benefits you had during your life, while the infinite loss is the loss of heaven or the afterlife, or whatever benefits come along with God's existence.  IF you wager that God does not exist, and God does not exist, then you've lost nothing and gained the benefits of having lived a life without the restrictions of religion.  

An easy way to think about this is by using poker.  If you play poker, and you're good at it, you should know about Pot Odds and Calculated Odds (or Hand Odds, or Winning Odds, or whatever you call it).  In effect, if your odds of winning are greater than your Pot Odds (the ratio of winning cards to the cards left in the deck), then you should bet.  Your chances are winning are greater, thus, than the cost in the case that you lose.  Theoretically, if you play by pot odds, you should end up winning more often than you lose.  

In Pascal's Wager, you would bet on God.  Your odds of winning are 1:1 (50%) because you cannot determine God's existence through reason (at least this is what Pascal is arguing, though he didn't believe that himself).  Your Pot odds are infinity:1.  Therefore, a logical person should bet on God's existence.  The point  may arise:  Well, what if I don't want to wager?  You must, according to Pascal.  The reason he believes this is because if you do not wager it has the same affect as if you had wagered against God.  Another way of putting it is this:  Imagine you're on a ship that's moving forward.  You see an island made of candy with waterfalls of alcohol.  You consider jumping ship, because you rather like candy and alcohol, however you're not a great swimmer.  While you are making your decision, the boat floats out of sight of the island.  Though you have not made a decision, the lack of a decision essentially decided it for you, because the decision was jump or not, and you did not jump, even though you had not decided not to jump.  The same goes with God. 

Now you, like I, may have noticed some problems with this.  The first minor problem, though glaring, is that it seems Pascal assumes a Christian God (and he does).  However, the same logic could apply to the God of many other religions, such as Islam.  Where the failure really lies is in the difference between wagering on God or not.  Let's say, for example, there is a Fluffy Marshmellow God.  He lives up in Candyland where the streets are made of chocolate and the clouds are balls of cotton candy.  What's more, Fluffy Marshmellow God doesn't care whether you believe in him or not.  You can come to Candyland either way.  For this type of God (whom I would rather like to believe in) there is no need to wager.   Thus, Pascal is assuming that God, if he should exist, must be a God that only allows eternal benefits to those who believe, which cannot be proven.  

A better problem is one of belief.  What Pascal is basically saying is that when you wager on God's existence, you're choosing to believe in him.  This assumes what is known as doxastic voluntarism.  In order for Pascal's Wager to be true, people have to be able to choose what they believe at will.  Without properly inspecting this, one might conclude that there's nothing wrong with this.  After all, you wouldn't believe something if you hadn't chosen to believe in it, right?  Well, yes and no.  You do, over time, change your beliefs and views, but this has more to do with changing beliefs at will.  For example, look at your hand.  Either one will do.  You know how many fingers you have, I'll assume most of those reading have five.  Now, believe there are six fingers on your hand.  Can you do it?  You can say you believe it, but you don't actually believe it because you can see plainly that there are only five.  This is an evidential belief because it's based on actual, sound, sufficient evidence.  Pascal's Wager, however, is based on pragmatic considerations.  So one can conclude from this that one ought not to base religious beliefs, nor any beliefs, on pragmatic considerations.  Beliefs should be based, rather, on sufficient evidence.  So Pascal can have his triangle and his law, but I, for one, would bet against his wager.   

Here's a follow up:  Follow Up on Pascal's Wager


 

9 comments:

Winton Bates said...

Very nice!

However, I think there is a chance that if Pascal pretended to believe and acted as though he believed, then he might actually come to believe.

If there is a God,I hope that he/she would be less impressed by such behaviour than by honest agnosticism.

The Whited Sepulchre said...

Agreed.
I've been reading about Pascal and his wager off and on for 40 years. This is the first time I've heard of Doxastic Voluntarism, although the meaning has to be explained any time Mr. Pascal's wager is refuted.

Anonymous said...

I think you made some valid points from a philosophical standpoint, although I'm not sure that you properly addressed the validity of the reasoning of Pascal's Wager.

The whole of Christianity is based on the concept of faith, which is completely opposite to the ideas you introduce about evidence. Pascal assumed there was a god and argued from there, you're doing the opposite. God is, by definition, unprovable. You're arguing against the validity of Christian tenents rather than the intellectual soundness of the "pot odds" argument. There is bias in your argument. It doesn't matter whether you go to hell because you chose not to believe or because you were unable to believe, the effect is the same.

The realisation I came to after mulling Pascal's wager over is that the argument tries to convince you of a world view but requires you to already have accepted the world view to accept the argument as valid. This doesn't make it any less true if heaven and hell do exist. It's a bad way to convert someone, but is it bad logic?

It isn't logic at all. Tt's a method of taking your beliefs and applying circular reasoning to reach the same conclusion. The best way to deal with Pascal's wager is to realise that when you bet on a god, you're betting that the ratio eternity:life is so large as to be undefined. When you bet on no god, you're betting that the ratio of life:afterlife (afterlife=0) is so large as to be undefined.

Either way, each bet risks everything if wrong and gains everything if correct. From an unbiased viewpoint, there is no dissimilarity and thus no way to prove or disprove the soundness of the argument itself without additional information.

Your point about the possibility of multiple gods is a subset of everything vs nothing idea. Even if you do consider the possibility of more than two ways to wager your life, it doesn't diminish the relative value of any two bets (christianity vs atheism for example), and so, draws no conclusion.

Pascal might have been wrong in the application of his reasoning (the idea that the choices were to either bet or abstain from betting), but his reasoning is neither right or wrong.

Anonymous said...

I chose the opposite of Pascal's wager - believing despite the promise of heaven. I doubt most would recommend this path.

Having faith is its own reward... even if I am subsequently damned for all eternity, or if nothing happens at all and I become food for worms in every sense, believing makes me something less of an animal.

Atheists (and fundies, I suppose) fail to even see the point of evolution. The fundies won't admit that it's real, and the atheists won't consider that evolution might have a higher purpose.

Dull witted people, both of them.

David said...

Anonymous,

I would love for you to enlighten me on the higher purpose evolution. Being dull witted I have a hard time seeing ahead a few billion years. Or have you been watching Stargate, and you've figured out how to ascend.

Lazy Slacker said...

I am agnostic, but I was trying to be as unbiased as I could. My parents are both journalists, though, so being unbiased doesn't come easily to me.

The Whited Sepulchre said...

Hey, Slacker.....

Did you get a few readers today ????

These blog hits were brought to you by The Traffic Building Ministry of The Whited Sepulchre and his Merry Band of Co-Redditors.

aestetix said...

Actually, you've missed the point. Pascal was making a case for how one lives, rather than what kind of god(s) exist.

To put the wager in different terms: let's say there is a specific way someone should live their life, and by living it so, they are rewarded with a pleasant afterlife. This makes no reference to God, but accomplishes the same goal. Now, obviously the wager assumes that believe in God is part of living this specific way, but his argument does not depend on which god(s).

With regards to the second point, you need to distinguish between a belief and a choice. First, your hand argument doesn't really work, since any non-academic will slap common sense back into you. A better example to use would be any kind symbol that triggers a reaction. I like using the swastika for this, because before the 20th century it was a very holy symbol and didn't have the negative connotations.

Your observation that our beliefs and views change over time is a good one. However, take into account societal norms, and how your views conflict with those of others. I may think gay marriage is acceptable, but there's no way I'm going to start arguments about it in a church.

It's easy to make a choice, but it's harder to back it up. This is why people generally let their social groups make those decisions for them. If I want to be a painter, I go live with a community of painters, and allow myself to be indoctrinated in their ideas. As you step through life, you become more acclimated to the ways of these painters, and less to that from which you came. One could say that as you get older, you have fewer choices, as you have more people and experiences which influence your decisions.

This is ultimately what Pascal is getting at when he says "choice".

Anonymous said...

Pascals triangle has little to do with geometry.

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