Phil1002 Problem set 2

The Pascal’s wager argument is also known as Gambler’s Argument, it is an argument for believing in the existence of God but not an argument for the existence of God. Pascal introduced a wager betting on the existence of God. It is an attempt to argue that it is reasonable to believe in the existence of God. There are practical reasons motivate a decision by the decision theory and probability theory.

I am going to explain Pascal’s wager argument in three parts: the assumption, the three main arguments and its conclusion.

There are two assumptions of the Pascal’s wager argument. The first assumption is that one does not know whether God exists. The theoretical reasons cannot decide or ever have enough evidence to show that the alternatives either God exists or that God does not exist. The disjunction can never be resolved through evidence gathered. Since God cannot be proved to exist, it is simply to give justifications for having the belief that God exists. Pascal's wager argument is not to prove that God exists, but only to gives affirmations for the belief in God.

Another assumption is that you must choose one alternative over the other. You are committed to place a bet on whether God exists or not. All of us need to make a decision whether accept that God exists or not. We have no option and we must play the bet. Pascal's wager argument had to weigh the two alternatives. Choosing one alternative over another will make a difference in your behavior and ultimately your livelihood.

The next part is the three main arguments in Pascal’s wager argument that show the justifications for having a belief in God and come to a conclusion that it is rational for you to wager for God.

The first argument is the Argument from Superordinance. Since there is no enough evidence to decide whether God exist or not need. It is a gamble for the uncertainty choice between accepting and rejecting the existence of God. The argument showed that all possible outcomes are considered in a decision under uncertainty while the probabilities of possible outcomes are not assigned.

You can either wager for God or wager against God and either God exist or God does not exist. The decision matrix helps you to decide the choice. There are four possible outcomes (gain or loss) to the gambler:

	God exists	God does not exist
Bet on God’s existence	Eternal life	Status quo
Bet against God’s existence	Eternal punishment	Status quo

If God exists, the bet on God’s existence will enjoy eternal life and happiness while the bet against God’s existence will suffer eternal damnation and hellfire. If there is no God, whether you bet on God’s existence or not, there is no afterlife.

Pascal came up with the different wager as an attempt to decide whether or not we should believe based on the possible outcomes for the afterlife. Even though God's existence is in question, acting as if God exists produces a better outcome. The bet on God’s existence is superdominant than the bet against the God’s existence and hence the most rational belief is belief in God.

The second argument is the Argument from Expectation. You are either to believe in God with the risk that he did not exist or not to believe in God risking to be condemned for eternity. The two alternatives are both under risk. The argument showed that the expectation is considered in a decision under risk so as to gain maximum expected utility.

A decision of bet on or against God’s existence is associated with a set of possible outcomes and each outcome has a certain value or utility. The expectation for each outcome is equal to its utility multiplied by the probability of its happening. The expectation for certain decision is the sum of the expectations for each possible associated outcome. Rationality requires you to place the bet of maximum expected utility. The two assumptions in this argument are that the probability of the existence of God is one-half and the wagering for God brings infinite reward if God exists.

Pascal assumed that there is equal risk of gain and of loss, it costs one life to wager for God and the utility is linear in number of lives. There are several cases that Pascal’s Wager argument suggested.

Considering the case that two lives is gained if you believe in God and God exists. You will have three lives if you win. You will lose you life that you have zero life.

The expectation(two lives gain) :

Probability(God exists) × the gain + Probability (God does not exist) × the loss = 0.5 ×3 + 0.5 ×0 = 1.5

Considering the case that there is infinite reward if you believe in God and God exists. You can gain an eternal life in heaven and have infinite lives if God exists and you win. You will lose our life if God does not exist and you lose.

The expectation(infinite lives gain):

Probability(God exists) × the gain + Probability (God does not exist) × the loss

= 0.5 × infinity + 0.5 × 0 = infinity

The expected utility indicated in unit of life is calculated.

	God exists	God does not exist
Bet on God’s existence	+ Infinity	0
Bet against God’s existence	1	1

If you choose not to believe in God, then you place your bet on lesser odds. If God does not exist, you will never know you made a mistake. If God does exist, and you gamble your life on God's non-existence, then you will give up an eternal thing lose eternal Heaven, happiness and life. In the argument, it shows that it is a wise bet to spend one life to win infinite lives with 50-50 odds. It is rational and warranted to have the bet on God’s existence.

Finally, the third argument is the argument form generalized expectations: Pascal’s Wager. There are two assumptions of this argument: it is reasonable to assign a finite value to P for the probability of God’s existence and it is reasonable always to act so as to maximize expected utility. You decide whether or not to bet on God or decide whether or not to believe in God is to consider the expected utility for each of these four options.

	God exists	God does not exist
Bet on God exists	Infinite	A1
Bet against God exists	A2	A3

The relative ranking of the utilities is likely to be as follows: A3 > A1 > A2. The bet against God’s existence if God does not exist, you win the gamble and enjoy finite happiness and live a life without illusion (A3). The bet on God’s existence if God does not exist, you loss the gamble and miss certain happiness (A1) as being a moral person. The bet on God’s existence if God exists, you loss the gamble and have a risk of eternal damnation (A2).

The bet on God’s existence will alter one's life to certain degree in the reduction of ease or happiness as well as devotion and sacrifice are the cost of betting on God’s existence. Considering the probability of God’s existence. A rational person will not deny there are finite probability that God exists no matter how small is the probability. The probability of God's existence is non-zero. It is supposed that the cost of making the bet is C and the probability assigned to the claim that God exists is P.

The following is the structure of choice in Pascal’s Wager Argument

Believe God exists Does not believe God exist

God exists God does not exist God exists God does not exist

(P) (1-P) (P) (1-P)

+Infinity-C - C - infinity 0

Considering the bet on God’s existence first.The expectation (bet for God’s existence) is:

=P ×(+ infinity- C) + (1-P) ×- C

= + Infinity

Considering the bet on God’s existence first.The expectation (bet for God’s existence) is:

=P ×(+ infinity- C) + (1-P) ×- C

= + Infinity

The probability of God exists is unlikely that it is exactly one-half, but this does not matter. Because the bet on God exists has the infinite value of expected utility, if God exists has any finite probability, the expectation for believing in God will be infinite. The potential gain of the bet on the existence of God is infinite, this standard favours the gamble as long as the probability of winning is non-zero.

Considering the bet against God’s existence. The expectation (bet for God does not exist)

= P × A2 (- infinity) + (1-P) × 0

= - infinity

According to Pascal's Wager argument, it is reasonable to bet on God’s existence because it has the higher expected utility and you risk eternal suffering in hell if you bet against God’s existence and loss. A rational person will always prefer and therefore choose that life which provides for his own greatest happiness and hence it is reasonable to conclude that one ought to bet on God’s existence.

Finally, I will explain the conclusion of Pascal’s Wager Argument. It is an argument for belief in God rather than as an argument for the existence of God. It is a demonstration of the practical reasons for the argument.

According to Pascal’s wager argument, betting on God is the correct alternative as a good gambler's rule is to minimize losses (pain and suffering) while maximizing gains (happiness) in a gambling situation. The expected utility gained by believing in God was much higher than by not believing. It is a good bet to choose the alternative God exists and act as if the alternative were true.

Pascal is supposed to establish the conclusion is to prove it is rationally warranted to believe the existence of God by the decision matrix because it is reasonable to make decisions on the basis of considerations of maximum expected utility. You are well-advised to become a believer, even if you do not believe that God exists, acting as if he did will produce benefits. The argument is intended to be directed towards people who already hold certain assumptions, and to convince these people that they ought to believe in God as the potential benefits of believing are so vast.

Choosing does not mean that we have to actually think that God exists, only that you act as if he does. Pascal agreed that belief is beyond what you can control. Although you want to believe the existence of God, you will not believe. Pascal suggested that the action and decision is what we can control. You cannot control the belief but you can try to believe it by acting as if you believe until you finally become the believer. We can take various practical steps and do certain types of actions (acting in a Christian way for example, go to church every Sunday, pray to God, be a morally good person, etc.) through entertaining beliefs about God and inducing the belief

Suppose an atheist philosopher believes very strongly that if God exists, non-believers will still go to Heaven because forgiveness is more important than punishment for a morally perfect God.

If the forgiveness is more important than punishment for a morally perfect God, all the people included the believers and non-believers will still go to Heaven. This is an objection of the decision matrix.

That mean the expected utility of the A2 will change from negative infinite to positive infinite. Both of the expectation of bet for and against God exists are the same. The decision matrix of the expected utility of the believer and non-believer will reconstruct as the following.

	God exists	God does not exist
Bet on God’s existence	Infinity	A1
Bet against God’s existence	Infinity	A3

The expectation (bet for God exists) is P ×infinity + (1-P) ×A1 = infinite number

The expectation (bet for God does not exist) is P ×infinity + (1-P) ×A3 = infinite number

When the expected utility is the same case in the believer and non-believer, the outcomes or the expectation for believers and non-believers are the same that they all go to heaven if such God does exist.

You make the decisions on the basis of considerations of maximum expected utility. In such case that either wager for or against god have the maximum expected utility. There is no difference whether the person believes or not and the Pascal’s Wager Argument is meaningless. There is no more reason to believe or not, so that the Pascal’s argument is irrelevant for this philosopher.

Reference :

1. http://plato.Stanford.edu/entries/pascal-wager

2. N.Warburton(1999), Philosophy: the basics, London, Routledge.P31-33

3. R.Nicholas(1985),Pascal’s Wager: A study of practical reasoning in philosophical theology, Notre Dame,University of Notre Dame Press.P1-19.

Hosted by www.Geocities.ws