That was Pascal's Wager.
Now, let's try and assess the argument
and see whether it's sound and potentially convincing
to the reasonable agnostic.
So one thing you might immediately be suspicious about
is premise two.
And there's a host of objections that people
have given to premise two.
Some of them-- There's a collection
that have very similar form.
And so let's consider those one by one here.
OK.
First, let's call this The Many Gods
Objection to Pascal's Wager.
So wait a second here.
We've made it out that I just have
two options: believing in God; being an Atheist,
not believing in God.
But in reality, there are many different gods,
in which I might choose to believe.
There's the Hindu god, the Christian god, the Muslim god,
the Jewish god, the Buddhist god.
There's tons of different gods.
Which of them should I believe in?
I mean, just as, say, we could've argued well,
as we did, that believing in the Christian god
had infinite expected utility.
That was what Pascal thought.
So the same kind of argument could
have been given for believing in the Hindu god.
Maybe if we believe in the Hindu god,
Hindu god will reward us with life in heaven.
Just as long as we think there is some chance that's correct,
then believing in the Hindu god has infinite expected utility.
And we can say the same for not just the established religions,
but all kinds of strange and imaginary gods.
Let's take the God of MIT.
You probably think there isn't a God of MIT.
But just so long as you think there's
some chance, albeit so unlikely, there just
has to be something, that there is
a God of MIT, who rewards believers
in the God of MIT with eternity in heaven,
then believing in the God of MIT will have
infinite expected value for you.
So what you really face is a whole array of options.
Believing in the Christian god, which
is what Pascal would've recommend that you believe in,
believing in the Hindu god, believing in the Buddhist god
and so forth, believing in the God of MIT,
believing in the God of the trees, believing in the God
of yourself.
There's a vast array of options.
And each one of them has infinite expected value.
So it's not so obvious that the right way
to respond to Pascal's argument is
to say the rational thing to do is to believe, as he did,
in the Christian god.
All it appears to say, for what we've said so far,
is that, in light of what he said,
you ought to believe in some god.
That's The Many Gods Objection to Pascal's Wager.
And it readily extends to an argument
that Pascal didn't really give us any reason
to believe in any god at all.
It's not just he didn't give us reason
to believe in the Christian god, as he did.
He didn't give us reason really to believe in any god at all.
Because just as we can't rule out the possibility
that there's a God of MIT, so we can't rule out the possibility
that there's a generous god.
What would a generous god be?
Well, a generous god would be a god who rewards believers
with life in heaven and then, when the non-believers
come to him, thinks, "Ah, I'll give them life in heaven too."
So believers and non-believers alike get life in heaven
from this generous god.
They get eternity in heaven.
Given that you can't rule out this possibility,
the outcomes associated with believing in god
are really these: First, there's you
living the life, a dissolute life, of a non-believer
and ceasing to exist.
That's it.
Second, there's your living the dissolute life
of a non-believer and then being given, in any case,
life in heaven.
Cool.
The probability you associate with the latter outcome,
call it P_GenerousGod.
It's the probability you associate
with there being a generous god, who's
going to give you life in heaven even
if you don't believe in him.
Just so long as that number is greater than zero, just so long
as you think there's some chance that there is such a god, then
the expected value for you of not believing
is, likewise, going to be infinite.
It's just the probability you associate
with a generous god multiplied by infinity.
That's some non-zero number multiplied by infinity,
plus the probability you associate
with there being no generous god multiplied
by the value for you of living a dissolute life followed
by no heaven.
And so both believing in God and not believing in God
will have infinite expected value.
So it's not particularly rational to believe in God
because, by doing so, you don't maximize expected value.
Third objection, The Weird Gods Objection to Pascal's Wager.
Does believing in God really have infinite expected utility?
Because just as you can't rule out the possibility
that there's a god who rewards believers in him
with life in heaven, nor can you really rule out the possibility
that there's a weird god who rewards believers in god
with an eternity in hell.
I mean, just as you associate some non-zero chance
with the former, so you're surely
going to associate some non-zero chance with the latter.
But supposing you do associate non-zero chance
with the latter, then there's a further outcome
that you need to consider when you're
trying to compute the expected value of believing in God.
That's this: Maybe you'll live the devout life of a believer
and go to hell.
The probability you associate with that,
call that the probability of there being a weird god,
P_WeirdGod, has to be multiplied by the value for you of your
living a devout life of a believer
and then going to hell.
Surely that's negative infinity.
So the expected value of believing in God
is going to turn out to be P_God multiplied
by infinity plus P_NoGod multiplied
by the value for you of living a devout life followed
by nothing, plus P_WeirdGod multiplied
by negative infinity.
Now, adding infinity to negative infinity is a tricky matter.
Typically, we say there's no number
that you get when you add infinity to negative infinity.
The value then, expected value, is undefined.
And indeed, the expected value of all the options open to you
here is going to be similarly undefined.
So it's not that by believing in God
you maximize expected value.
Believing in God has no defined expected value.
In reply to these three objections,
a follower of Pascal could say this:
Look, when infinite costs and benefits are at stake,
it's not like the only rational imperative
is to maximize expected value.
That's clearly not right.
So suppose that I was to offer you two options.
Option one, you get to go to heaven.
There's an afterlife and you get to go to heaven.
OK?
That's pretty great.
You have an eternity of heaven that you're faced with.
Option two, there's an afterlife,
and I'll give you a one in six chance of spending all of it
in heaven.
It doesn't seem like a very hard choice.
I mean, which option should you take?
Of course, you should take the first option.
Anybody would take the first option.
Any rational person would take the first option.
First option clearly beats the second one.
And yet, of course, the way we've defined expected value up
to now, the first option has infinite expected value.
The second option has infinite expected value.
Expected value of the first is just one times infinity.
Expected value of the second is just 1/6 times infinity plus
5/6 times whatever value you associate
with not spending eternity in heaven.
Infinite either way.
So any account of rationality that says all you've got to do
is maximize expected value is clearly
a bad account of rationality.
I just gave an example of a case where there's clearly
one option that's the rational one to take,
even though it's not the option that maximizes the expected
value.
So in these cases, where infinite rewards are at stake,
we need to expand upon our account of rationality.
The natural way to do it is this:
So if there's some number, n, such
that if we set the value of the infinite reward at n,
then the expected value of a particular option
is greater than the expected value of all other options.
And furthermore, if we set the value of the infinite reward
at any finite number higher than n,
then the expected value of that same option
comes out as higher than the expected value
of all other options.
Then we rationally ought to take that first option.
It's a bit of a complicated idea,
but it gives us the right results,
which is that you ought to take the certain eternity
of a heaven over the 1/6 of a chance of eternity in heaven.
And it gives us a response to these many gods, weird gods,
punitive gods, generous gods, objections to Pascal's Wager.
Because it's going to turn out that, just so long as you think
it's very slightly more likely that you'll get eternity
in heaven if you believe in a particular kind of god,
rather than doing anything else, believing
in another kind of god or not believing in God,
then that is rationally what you ought to be doing.
You rationally ought to be doing this thing, the thing that
gives you the best chance, no matter how small,
of getting to heaven.