An exploration of Pascal’s Wager
Blake Smith
Philosophy of Religion
(Comic by XKCD found at http://www.xkcd.com/525/ )
If one asks a theist, and in America this is usually a Christian theist of some
denomination, the answer they will give often sounds a little something like this: “I would rather
take my chances believing in God, just in case I die and he does exist.” This is a common
argument, and a compelling argument when one considers what might be at stake in such a
gamble. This argument is common and has some variety in how people say it, but a
mathematician already modeled the wager very concisely, and perhaps, more convincingly than
the common theist’s wording. The argument is simply known as Pascal’s Wager, where Pascal
claims that rationality should lead one to place their bet on God’s existence when gambling with
the fate of their eternal soul. In the course of this paper, I intend to explore Pascal’s Wager
thoroughly, taking a tour through both sides of the wager and then decide how convincing it is.
Pascal argues not for a proof of God’s existence because he claims God’s existence to be
unknowable. “Endeavour ... to convince yourself, not by increase of proofs of God...”1 Instead,
one should try to understand the consequences of choosing belief or disbelief in God, and then
take a gamble on the idea. The argument has been beautifully modeled this way:
(1) It is possible that the Christian God exists and it is possible that the Christian God does not exist.
(2) If one believes in the Christian God then if he exists then one receives an infinitely great reward and
if he does not exist then one loses little or nothing.
(3) If one does not believe in the Christian God then if he exists then one receives an infinitely great
punishment and if he does not exist then one gains little or nothing.
(4) It is better to either receive an infinitely great reward or lose little or nothing than it is to either
receive an infinitely great punishment or gain little or nothing.
Therefore:
(5) It is better to believe in the Christian God than it is not to believe in the Christian God.
(6) If one course of action is better than another then it is rational to follow that course of action and
irrational to follow the other.
2
Therefore:
(7) It is rational to believe in the Christian God and irrational not to believe in the Christian God.
1
2
Summary and explanations of Pascal’s arguments found at http://plato.stanford.edu/entries/pascal-wager/
Pascal’s Wager argument found at http://www.philosophyofreligion.info/theistic-proofs/pascals-wager/
So it seems that by this argument, there are a few different concepts I have to consider
before I take my bet on God’s existence, and being a careful person who doesn’t fancy himself a
gambler, I want to fully understand these concepts and take the safest bet. The way these
premises are set up might be visualized with a decision matrix:
1. Either God exists or God does not exist, and you can either wager for God or
wager against God. The utilities of the relevant possible outcomes are as
follows, where f1, f2, and f3 are numbers whose values are not specified
beyond the requirement that they be finite:
God exists God does not exist
Wager for God
∞
f1
Wager against God
f2
f3
3
By looking carefully at this matrix, I should consider my choices under the conditions of God
existing and not existing.
Suppose God does not exist, and I choose not to believe in him. (f3) I might have an
amazing life filled with sex, drugs and rock and roll, without any worry of damnation. I might
get away with all kinds of sinful pleasures like holding hands on the first date, or parking in a
handicapped zone because I’m basically Hitler. I might add up the values of each hedonist
pleasure and place a value into the table, so long as it is not infinite, let’s say 1,000,000 “units”
of hedonism, because I had a really great life of partying and drinking and got really rich
investing in antitheist literature or something. I would place in the box (1,000,000).
Now suppose God does not exist, and I innocently wager for God’s existence. (f1) What
might the repercussions be? In Christianity, depending on the sect, believing in God comes with
it some contingencies, for argument’s sake, I should find the sect with the strictest stipulations on
3
Table found at http://plato.stanford.edu/entries/pascal-wager/#4
Christian belief. I would look no further than the LDS Church for an example. I use this example
mostly because of my own sick humor, but the idea of “strict” is a rather subjective term so I
chose a church that institutionalizes it’s theology through a tight bureaucracy. If I wanted to go
to the Brigham Young University for instance, a university privately owned by the LDS Church,
I would need to follow the very strict Honor Code4 in place at the campus. One of the major
requirements of this code is to be in good standing with the Church itself. I would have to follow
strictly the Word of Wisdom5 and the Articles of Faith6, as well as actively engage in Church
activities in order to get an official recommendation from the Church authorities. The standards
for living set by the LDS church are rather restrictive, and might lead to a quite depressing life
under the most extreme circumstances. Some examples being bans on sexual activity, smoking,
coffee, tea, alcohol, curse words, beards, and having the misfortune of being homosexually
inclined. I’ll be really extreme and score this life (-1,000,000).
Now, let’s assume that God did exist in these situations. If I was to have my awesome life
of disbelief and God damned me to Hell for all the sex, drugs and parking in handicapped spaces,
I might say that my eternal afterlife would be pretty terrible for not believing. I am, after all
talking about a life in hell, or in LDS theology, the third kingdom of heaven far away from God’s
glory. Let’s Give this a score of (-∞) (f2).
4
BYU Honor Code found at http://registrar.byu.edu/catalog/2014-2015ucat/GeneralInfo/HonorCode.php
Word of Wisdom found at https://www.lds.org/topics/word-of-wisdom?lang=eng
6
Articles of Faith full list at this terribly long url: http://media.ldscdn.org/pdf/lds-magazines/liahona-december2011/2011-12-30-the-articles-of-faith-of-the-church-of-jesus-christ-of-latter-day-saints-eng.pdf
5
Now then, with all of these data points hypothesized, I’ll fill out the table by replacing the
variables with the values I have given the potential possibilities.
God exists
God does not
exist
Wager for God
∞
-1,000,000
Wager against God
-∞
+1,000,000
By looking at this data, it is clear that the most fertile reward comes from wagering in
favor of God’s existence, and the greatest risk would be wagering against God. The hedonic cost
of wagering for God is pennies compared to the ultimate cost of eternal damnation, and the
pleasure of a life wagering against God is infinitesimally small in comparison to an afterlife in
heaven. Based on this, we can safely say that Pascal’s conclusion that it is rational to believe in
God, is true.
The problem seems to pop up for me right away, however, when Pascal says he is
explicitly referring to the Christian God. There are so many different religions and with them,
many different ideas about God and his/her/its existence. My question to Pascal would be “What
makes the Christian God so much more threatening or rewarding than the other religions?
Certainly if God’s existence in unknowable, then it seems it could just as easily be that wagering
for God’s existence could seal my eternal damnation if the personality of God is different from
how I believe it to be. Perhaps that is the major flaw with this argument, in that it is infected with
a scope problem. Any God may be injected into the argument and it would suffice. For example,
if I wager for the existence of Satan, and believing in Satan requires me to burn churches a drink
unicorn blood, then it would be in my best interest to wager on Satan, for he would reward me in
the end. This wager would be in direct contradiction with wagering for the Christian God, and no
part of Pascal’s argument seems to justify the exclusive use of the Christian God. But even for
argument’s sake, I’ll embrace the “Christian God.” To make this point stunningly clear, there are
many different Christian denominations, most of which have uniquely distinct rules and ideas
about what belief in God requires.7 8 This makes it difficult to hold with any certainty that the
argument can or should be used to promote personal faith, because if anyone uses this to promote
faith in the God of their denomination, it gives no certainty that they are not sealing their fate in
hell under another denomination’s rules, which they may have just as easily wagered for. And in
some religions, it would be possible to have a great life, and still get into heaven in the afterlife,
changing the table dramatically. Adding this to Pascal’s wager might make getting into heaven
feel more like playing a high-stakes lottery, where all the incorrect guesses get your house
burned down, and the winner receives a private island.
To conclude, I would have to say that I am just as lost in terms of belief in God as I was
before I read Pascal’s wager. The argument is simple and elegant, but for a skeptic, seems to lack
any useful information in deciding which God to believe in. The stakes in this gamble are high,
and some might justly choose not to play.
7
List of different Christian denominations http://undergod.procon.org/view.backgroundresource.php?resourceID=87
8
Different interpretations of the 10 commandments http://undergod.procon.org/view.backgroundresource.php?resourceID=824