Sunday, September 03, 2006

Pascal's Wager

This is an old argument thought up by the French physicist, mathematcian and philosopher Blaise Pascal. I'd be interested to see people's thoughts on it.

It's not meant to be an argument that says Christianity is true - Pascal helped invent probability theory in maths; it's meant to be an argument about which way is the better bet, Christianity or atheism.

The Argument

The argument basically goes like this...

Lets assume there are only two possibilities for belief - Christianity and Atheism and that one and only one of them is correct. For the sake of argument, lets say that the probability of the Christians being correct is p, so the probability of the Atheists being correct is 1-p.Each belief has a group of people who follow it - the Christians and the Atheists.

If Atheism is correct, then both groups will end up exactly the same - pushing up the daisies. If Christianity is correct, then the Christians will end up very much better off than the Atheists. Lets call the amount the Christians will be better off than the Atheists in this scenario H.

So the Christians stand chance p of gaining H - their expected gain is pH.

The Atheists, by contrast, have no expected gain. Whether they are right or not, they do not end up better off than the Christians. So, said Pascal, if you're betting, it's much better to bet on being a Christian than an Atheist.


The usual criticisms I hear of Pascal's Wager go something along these lines:

1. Probability theory doesn't work on this.

2. Pascal only gets the results he does because he has massively oversimplified the situation. There are far more possibilities than just Christianity and Atheism. And surely leading a good life has to count for something, even if I don't believe in God.

3. It doesn't work, because Atheists get to make the most of their life now, whereas Christians are busy worrying about the next one.

My Analysis

I don't understand 1. Why shouldn't probability theory work on this?

2. really doesn't work either. Yes, you could introduce other ideas - Islam, Buddhism, etc. But it wouldn't change the fact that Christians end up better off than Atheists on average unless you start introducing silly religions that treat Atheists better than Christians in the afterlife, and give them a higher probability than Christianity. I don't see any of those religions around, and I don't think I've ever heard any arguments for their validity... Of course, you might decide that Islam (for example) comes out as an even better bet, but that doesn't change the fact that Christianity comes out better than Atheism

The third objection is better. Being a Christian does cost stuff in this life (but also, I think, makes this life a lot more livable). Lets say that being a Christian in this life costs an extra amount c compared to being an Atheist.

In that case, Christians would gain pH and lose c, so their expected gain would be pH - c. Atheists would still have zero gain.

So in order for Atheism to be a better bet than Christianity, c > pH. In other words, the cost of being a Christian would have to be bigger than the probability of Christianity being true multiplied by the gain Christians get if they are right in the afterlife.

In other words, to be an Atheist rather than a Christian, you are either very poor at betting or sure of at least one of the following options:

  • that it would cost an immense amount to be a Christian, so great that even a decent chance of an eternity of paradise would not make up for it
  • the chance of Christianity being true is vanishingly small (to which I would say that if so many otherwise sensible people believe it, it's not going to be that unlikely)
  • the promised reward in Christianity is not that great.

So what do people think? Which is it?

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