You have two things to lose: the true and the good; and two things to stake: your reason and your will, your knowledge and your happiness. Since you must necessarily choose, your reason is no more affronted by choosing one rather than the other. But your happiness? Let us weigh up the gain and the loss involved in calling heads that God exists.
Let us assess the two cases: if you win you win everything, if you lose you lose nothing. Do not hesitate then; wager that he does exist. But here there is an infinity of happy life to be won, one chance of winning against a finite number of chances of losing, and what you are staking is finite. Finally, it may be that a genuine option is one that possesses sufficient evidential support, in which case it can then participate in a run-off decision procedure.
Some Pascalians propose combining pragmatic and epistemic factors in a two-stage process. First, one uses epistemic considerations in selecting a limited set of belief options, then one uses prudential considerations in choosing among them Jordan b.
Alternatively, one first uses prudential considerations to choose religion over non-religion, and then uses epistemic considerations to choose a particular religion Schlesinger , Jordan In order to be at all plausible, this approach must answer two questions. First, what is the justification for deliberately excluding some possibilities, no matter how improbable, from prudential reasoning? It seems irrational to dismiss some options that are acknowledged to be possible, even be they unlikely, so long as the stakes are sufficiently high Sorensen Second, can epistemic considerations work without begging the question?
Schlesinger argues that the Principle of Sufficient Reason gives some support for believing in God, but in a Pascalian context this is questionable. But the Crusades in the s taught the French of Islam, the Renaissance in the s taught the French of Greco-Roman paganism, the discoveries of the s taught the French of new-world paganism, and several wars of religion taught the French of Protestantism.
To claim that the educated French of the s rightfully rejected alien beliefs without consideration appears to endorse rank prejudice. The idea is that Catholics, Protestants, Jews, Moslems, and devil-worshippers can all legitimately use decision theory to conclude that it is best to believe in some supreme being.
Against this there are two objections. But consider the following sort of atheistic Buddhism: if you clear your mind then you will attain nirvana and otherwise you will not — that is, if you fill your mind with thoughts and desires, such as believing that God exists or living God, then you will not attain salvation Saka There are two versions of this objection that need to be kept distinct. Schlesinger responds by saying that any reasoning that gets us to believe in God, if God exists, cannot be bad.
But this argument seems to depend on the nature of God. If God holds that results are all that matter, that the ends justify the means, then Schlesinger is right. But maybe God holds that true beliefs count as meritorious only if they are based on good evidence; maybe God rewards only evidentialists. In short, this form of the objection is just another version of the many-gods objection. Moore — for us to base any belief on decision-theoretic self-interest Clifford , Nicholls Since utilitarians would tend to favor Pascalian reasoning while Kantians and virtue ethicists would not, the issue at stake belongs to a much larger debate in moral philosophy.
If you regularly brush your teeth, there is some chance you will go to heaven and enjoy infinite bliss. On the other hand, there is some chance you will enjoy infinite heavenly bliss even if you do not brush your teeth. While the Wager has its advocates, there are many objections. There are many religions, and believing in the God of one religion might prevent gaining the infinite rewards of another religion.
Assuming the probabilities of Christianity, Islam, and atheism are greater than zero, we get confusing expected values. You might think the decision matrix tells us that believing either religion is a better bet than believing atheism.
Thus, all options seem to have the same expected value. A common response to the many-gods objection can be summarized in two words: probability matters. It matters even when dealing with infinite values. Christianity and Islam actually do not have the same expected value—wagering on the more probable religion gives you a higher chance at an infinite good, and so has a higher expected value.
Most philosophers reject doxastic voluntarism , the view that we can directly control our beliefs. This might be indirect control, like the control you could exercise over your political beliefs by changing the news sources you read. A second response—which Pascal himself favored—frames the wager in terms of action , rather than belief. The wager gives you a reason to commit to God—by going to church, praying, and immersing yourself in a religious community—rather than trying to directly believe in God.
It seems like forming a belief on the basis of a wager would violate evidentialism , the view that we should proportion our beliefs to the evidence. We should believe because of evidence, not because a belief is beneficial. This is because more than one belief-attitude fits your evidence. It is typical to present these numbers in a decision matrix, with the columns corresponding to the various relevant states of the world, and the rows corresponding to the various possible actions that the agent can perform.
In decisions under uncertainty , nothing more is given—in particular, the agent does not assign subjective probabilities to the states of the world. Still, sometimes rationality dictates a unique decision nonetheless.
Consider, for example, a case that will be particularly relevant here. In decisions under risk , the agent assigns subjective probabilities to the various states of the world. Assume that the states of the world are independent of what the agent does. According to decision theory, rationality requires you to perform the action of maximum expected utility if there is one. Suppose that the utility of money is linear in number of dollars: you value money at exactly its face value. Suppose that you have the option of paying a dollar to play a game in which there is an equal chance of returning nothing, and returning three dollars.
The expectation of the game itself is. This exceeds the expectation of not playing namely 0 , so you should play. On the other hand, if the game gave an equal chance of returning nothing, and returning two dollars, then its expectation would be:. Then consistent with decision theory, you could either pay the dollar to play, or refuse to play, for either way your overall expectation would be 0. It should be admitted that there are certain exegetical problems in presenting these arguments.
Furthermore, our formulation of the arguments in the parlance of modern Bayesian decision theory might appear somewhat anachronistic. For example, Pascal did not distinguish between what we would now call objective and subjective probability, although it is clear that it is the latter that is relevant to his arguments. There is the further problem of dividing the Infinite-nothing into separate arguments. We will locate three arguments that each conclude that rationality requires you to wager for God, although they interleave in the text.
We will conclude with a discussion of what Pascal meant by this. Reason cannot settle which way we should incline, but a consideration of the relevant outcomes supposedly can. Here is the first key passage:. There are exegetical problems already here, partly because Pascal appears to contradict himself. If it could, then it might well be shocked—namely, if you chose in a way contrary to it. Wagering for God superdominates wagering against God: the worst outcome associated with wagering for God status quo is at least as good as the best outcome associated with wagering against God status quo ; and if God exists, the result of wagering for God is strictly better than the result of wagering against God.
The fact that the result is much better does not matter yet. Pascal draws the conclusion at this point that you should wager for God. Rationality does not require you to wager for God if you assign probability 0 to God existing, as a strict atheist might.
If that is a further premise, then the argument is apparently valid; but that premise contradicts his subsequent assumption that you assign positive probability. See McClennen for a reading of this argument as a decision under uncertainty. Pascal appears to be aware of a further objection to this argument, for he immediately imagines an opponent replying:. The thought seems to be that if I wager for God, and God does not exist, then I really do lose something.
In fact, Pascal himself speaks of staking something when one wagers for God, which presumably one loses if God does not exist.
Pascal addresses this at once in his second argument, which we will discuss only briefly, as it can be thought of as just a prelude to the main argument. Now, recall our calculation of the expectations of the two dollar and three dollar gambles. This is, as it were, a warm-up. 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 an eternity of life salvation.
One way to defend it is via the classical interpretation of probability, according to which all possibilities are given equal weight. However, unless more is said, the interpretation yields implausible, and even contradictory results. In the lottery ticket case, reason can decide something.
But it is not clear that complete ignorance should be modeled as sharp indifference. Morris imagines, rather, an agent who does have evidence for and against the existence of God, but it is equally balanced. This argument, then, does not speak to them. This brings us to the third, and by far the most important, of his arguments. Again this passage is difficult to understand completely. In short, if God exists, then wagering for God results in infinite utility.
What about the utilities for the other possible outcomes? Martin among others assigns this a value of negative infinity. Sobel , on the other hand, is one author who takes this value to be finite. This suggests that whatever these values are, they are finite. In another landmark moment in this passage, he next presents a formulation of expected utility theory.
How much, then, should a player be prepared to stake without transgressing against reason? Let us now gather together all of these points into a single argument. Either God exists or God does not exist, and you can either wager for God or wager against God. We have a decision under risk, with probabilities assigned to the ways the world could be, and utilities assigned to the outcomes.
On the other hand, your expected utility of wagering against God is. This is finite. Therefore, rationality requires you to wager for God. Here the objections are manifold. Different matrices for different people. The argument assumes that the same decision matrix applies to everybody. However, perhaps the relevant rewards are different for different people.
Perhaps, for example, there is a predestined infinite reward for the Chosen, whatever they do, and finite utility for the rest, as Mackie suggests. Or maybe the prospect of salvation appeals more to some people than to others, as Swinburne has noted. This brings us to the next two objections. The utility of salvation could not be infinite. One might argue that the very notion of infinite utility is suspect—see for example Jeffrey and McClennen Strict finitists, who are suspicious of the notion of infinity in general, will agree—see Dummett and Wright Or perhaps the notion of infinite utility makes sense, but an infinite reward could only be finitely appreciated by a human being.
There should be more than one infinity in the matrix. There are also critics of the Wager who, far from objecting to infinite utilities, want to see more of them in the matrix. For example, it might be thought that a forgiving God would bestow infinite utility upon wagerers-for and wagerers-against alike—Rescher is one author who entertains this possibility.
Or it might be thought that, on the contrary, wagering against an existent God results in negative infinite utility. As we have noted, some authors read Pascal himself as saying as much. Suppose, for instance, that God does not exist, but that we are reincarnated ad infinitum , and that the total utility we receive is an infinite sum that diverges to infinity or to negative infinity. The matrix should have more rows.
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