Blaise Pascal's Bet on God

[Guest guest]

Many "proofs" for the existence of God were invented during the times

of the Christian scholasticists. One such "proof" was offered by the

famous mathematician and philosopher, Blaise Pascal (1623-1662).

 

Pascal argued that a rational person ought to believe in the existence

of God because of mathematical probability considerations. Though we

may not know for sure whether God exists, we can consider our belief

(or lack of it) as a bet on God's existence, the outcome of which can

be computed as follows.

 

Let the probability that God does not exist be p;

the probability for God's existence will, therefore, be 1 - p.

 

We have, then, these possibilities:

 

1. if we believe in God, and God does not exist, we will have passed

up some worldly pleasures as a consequence of our mistaken belief in

Him, at a cost represented by -c (a negative quantity because it is

akin to an expenditure).

2. if we believe in God, and God does exist, we receive a heavenly reward r.

3. if we do not believe in God, and God does not exist, we have

neither gained nor lost; the outcome is 0.

4. if we do not believe in God, and God does exist, there may be some

punishment meted out to us, perhaps some time to serve in hell. Let

us denote these costs as -h (negative again, for the same reason as

above). In case there is no punishment for not believing, h will

equal 0.

 

Now we can set up the equations for the outcomes of our bet:

 

If we believe in God, the outcome is the probability-weighted sum of cases 1 and 2:

p.(-c) + (1-p).r

 

If we do not believe in God, the outcome is the probability-weighted sum of cases 3 and 4:

p.0 + (1-p).(-h)

 

But since the quantity r will, by definition, be infinite, the outcome

of the first equation will always be greater than that of the second

equation, no matter what probability we assign to p for the existence

of God. Therefore, the only rational strategy that we have for our bet

is to believe in God.

 

It is interesting to note that Pascal did not need to make any

assumptions on the finiteness of h because of the negative sign of

that quantity.

 

Michael