Pascal's Wager is a decision theory based method written by French philosopher Blaise Pascal in an attempt to suggest that of all possible outcomes it is better believe in the Christian God than not to. Aside from alternate interpretations of the wager, a major flaw exists in his reasoning known as the fallacy of false dilemma.


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    State Pascal's Wager. If God exists (G) and you believe in him (B), then the reward is heaven (+Infinity). If God exist (G) and you don't believe in him (~B), then the reward is eternal damnation (-Infinity). If God does not exist (~G) and you don't believe in him (~B), then you gain nothing (+0). If God does not exist( ~G) and you do believe in him (B), then you lose nothing. In order to evaluate Pascal's Wager, we calculate the marginal outcome for each case over which you have control (B or ~B) by summing over all the cases where you do not have control (G or ~G). Notice that, if Pascal's Wager is correct, the reward for believing in God is infinitely good and the reward for not believing in him is infinitely bad.

G ~G Outcome
B +∞ -0 +∞
~B -∞ +0 -∞
Image titled Discount Pascal's Wager Step 1
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    Consider that if B & ~G (you believe in God and he does not exist), you actually do lose something. For example, you might consider your time praying or in church wasted or your faith might require dietary restrictions, such that you might never be able to eat pork, beef, or shellfish. Consider a more severe example, Jehovah's Witnesses' faith requires that they not receive blood transfusions. If B & ~G and you require a life-saving blood transfusion, then, by not accepting such a transfusion, you have made a large sacrifice indeed. These sacrifices, however, are small relative to the infinite magnitudes associated with G, so we can denote them with an arbitrary constant, say, 1. Notice that this does not change our outcome.
G ~G Outcome
B +∞ -1 +∞
~B -∞ +1 -∞
Image titled Discount Pascal's Wager Step 2
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    Consider the possibility that God exists, but you have chosen the incorrect God. Let us denote this as event W. Understandably, this God would be upset that you have been worshipping the wrong God. However, he still disapproves of non-believers. This is the first example of the false dilemma. That is, Pascal has not considered all possible cases beyond his control. This alone is enough to discount Pascal's Wager, but we will continue in order to show that we assign any arbitrary value for the outcome.
G ~G W Outcome
B +∞ -1 -∞ -1
~B -∞ +1 -∞ -∞
Image titled Discount Pascal's Wager Step 3
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    Consider the possibility that God exists, but God is the Flying Spaghetti Monster. The Flying Spaghetti Monster hates believers because he has left no evidence of his existence and considers them foolish for believing in things without evidence. We will denote this as event FSM. Now, our analysis has completely failed because, no matter what we believe, the expected results are infinitely bad.
G ~G W FSM Outcome
B +∞ -1 -∞ -∞ -∞
~B -∞ +1 -∞ +∞ -∞
Image titled Discount Pascal's Wager Step 4
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    Consider the possibility that God truly is all-loving and that our wagerer has led a good life. In this case, the reward is the same for the wagerer in either B or ~B. We denote this as case L. In this case, it is better to be a non-believer than a believer.
G ~G W FSM L Outcome
B +∞ -1 -∞ -∞ +∞ -1
~B -∞ +1 -∞ +∞ +∞ +1
Image titled Discount Pascal's Wager Step 5
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    Finally, consider the case of a similar God to that described by event L, except that this God despises those that accept Pascal's Wager, considering it demeaning to him. In this case, which we denote H, it is infinitely better to be a non-believer than a believer.
G ~G W FSM L H Outcome
B +∞ -1 -∞ -∞ +∞ -∞ -∞
~B -∞ +1 -∞ +∞ +∞ +∞ +∞
Image titled Discount Pascal's Wager Step 6
  1. Image titled Discount Pascal's Wager Step 7
    Realize that one can add infinitely many possible categories of God. The choices here are arbitrary, and Pascal's Wager can be used to suggest any outcome desired. It is, therefore, not an acceptable method for determining whether one should believe in God in the absence of evidence. See the warnings section for information about how our analysis is incorrect.


  • Real decision theory would include as much information as possible about the probability of each event. Pascal suggested infinite reward and punishment which negates the effects of probability (∞ times any non-zero positive number is infinity, ∞ times zero is undefined).
  • Although you may not agree with the suggested categories of God, you do not have an evidence to the contrary. Even if you did (assigning the probability of certain cases to zero), this would lead to undefined results (see above). In fact, our results are not correct either because we have tacitly done this for the cases that are not included in the table. A correct interpretation would reveal that the outcome is undefined for either case (B or ~B).
  • Decision theory is very effective in cases where there is not a false dilemma and outcomes are finite. Do not discount its methods when they are applicable.
  • Mathematics frowns upon the use of infinities in this manner. However, a calculus based approach involving limits would make the article longer than it already is and the results would turn out the same.
  • Flying Spaghetti Monsterism is a parody religion designed by atheists to be completely analogous to a living religion in order to demonstrate the inanity of the intelligent design movement. It's admission that it is not factual does not discount its inclusion in this analysis in the same sense that one must also consider case W and that most theists would argue that their faith is the one true faith and all others are inane. FSMism is included to lessen the abstract nature of this analysis, other religious ideas could be substituted.

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Categories: Faith and Belief