2nd Argument

The uncertainty of the decision lead to the second argument: a Pascal’s wager is a decision situation in which the possible gain or benefit involved in one of the outcomes swamps all the others. With Pascal’s wager, the possible gain of theism is supposed to be not just greater than that of nonbelief, it is of a cardinality infinitely greater. Because attached to theistic belief is nonpareil. It is not a religious topic. It is a swamping property as involving not an infinite value only but as a gain that is vastly greater than any of its rivals. This gain is so great as to render the probability assignments, even if they are known, virtually irrelevant.

The second argument is the Argument from Expectation. It is an argument that we should consider the expectation when you make a decision under risk so as to gain maximum expected utility.

A certain decision or action 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 a given action is the sum of the expectations for each possible associated outcome. The course of action having the maximum expectation is the rational one to follow.

When you make the decision under risk, you should calculate the expected utility that is the expectation of a given action produces in that state by the state’s probability. According to decision theory, rationality requires you to perform the action of maximum expected utility.

The three assumptions in this argument are:

1.there is equal risk of gain and of loss(the probability of the existence of God is one-half)

2.the wagering for God brings infinite reward if God exists.

3.I

His hypothetically speaking of "two lives" and "three lives" may strike one as odd.There are several cases that Pascal’s Wager argument suggested.

Case 1: Win: gain one extra life = have two lives

Lose: lose your life=have zero lives

The expectation (one life gain) :

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

= 0.5 ×2 + 0.5 ×0 = 1

Since the expectation just equals the entry fee," you might still play or you might not."

Case 2: Win: gain two extra lives = have three lives

Lose: lose your life=have zero lives

The expectation (two life gain):

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

= 0.5 ×3 + 0.5 ×0 = 1.5

Since the expectation exceeds the entry fee, "you would be imprudent" not to accept this gamble.

But consider now 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.

Case 3: Win: gain eternal life(in heaven) = have infinitely lives

Lose: lose your life=have zero lives

The expectation (eternal life gain) :

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

= 0.5 ×infinity + 0.5 ×0 = infinity

Since wagering for God is rationally required even in the hypothetical case in which one of the prizes is three lives, then all the more it is rationally required in the actual case, in which one of the prizes is eternal life .Provide there is some finite chance of winning, however small, the expectation infinitely exceeds the entry fee, and the gamble should be run.

The expected utility indicated in unit of life is calculated. The decision matrix is as the following.

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

Since the top alternative has an infinite expectation regard less of the probability, while its rival has the uniform expectation of a single unit, betting on God is clearly the best plan. "There is no need to hesitate; you must risk all."

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.

However, Pascal realizes that the value of 1/2 actually plays no real role in the argument, thanks to (2). This brings us to the third, and by far the most important, of his arguments.

3rd argument: Pascal’s Wager

Reference:

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

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

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

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