Zero Probability as it relates to Empiricism
Pascal maintains that we are incapable of knowing whether God exists or not, yet we must “wager” one way or the other. Reason cannot settle which way we should incline, but a consideration of the relevant outcomes supposedly can. Here is the first key passage:
Following McClennen 1994, Pascal’s argument seems to be best captured as presenting the following decision matrix:
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.
Without any assumption about your probability assignment to God’s existence, the argument is invalid. Rationality does not require you to wager for God if you assign probability 0 to God existing, as a strict atheist might. And Pascal does not explicitly rule this possibility out until a later passage, when he assumes that you assign positive probability to God’s existence; yet this argument is presented as if it is self-contained. His claim that “[r]eason can decide nothing here” may suggest that Pascal regards this as a decision under uncertainty, which is to assume that you do not assign probability at all to God’s existence. 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:
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.
“God is, or He is not.” But to which side shall we incline? Reason can decide nothing here. There is an infinite chaos which separated us. A game is being played at the extremity of this infinite distance where heads or tails will turn up… Which will you choose then? Let us see. Since you must choose, let us see which interests you least. 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; and your nature has two things to shun, error and misery. Your reason is no more shocked in choosing one rather than the other, since you must of necessity choose… But your happiness? Let us weigh the gain and the loss in wagering that God is… If you gain, you gain all; if you lose, you lose nothing. Wager, then, without hesitation that He is.There are exegetical problems already here, partly because Pascal appears to contradict himself. He speaks of “the true” as something that you can “lose”, and “error” as something “to shun”. Yet he goes on to claim that if you lose the wager that God is, then “you lose nothing”. Surely in that case you “lose the true”, which is just to say that you have made an error. Pascal believes, of course, that the existence of God is “the true”—but that is not something that he can appeal to in this argument. Moreover, it is not because “you must of necessity choose” that “your reason is no more shocked in choosing one rather than the other”. Rather, by Pascal’s own account, it is because “[r]eason can decide nothing here”. (If it could, then it might well be shocked—namely, if you chose in a way contrary to it.)
Following McClennen 1994, Pascal’s argument seems to be best captured as presenting the following decision matrix:
| God exists | God does not exist | |
| Wager for God | Gain all | Status quo |
| Wager against God | Misery | Status quo |
Without any assumption about your probability assignment to God’s existence, the argument is invalid. Rationality does not require you to wager for God if you assign probability 0 to God existing, as a strict atheist might. And Pascal does not explicitly rule this possibility out until a later passage, when he assumes that you assign positive probability to God’s existence; yet this argument is presented as if it is self-contained. His claim that “[r]eason can decide nothing here” may suggest that Pascal regards this as a decision under uncertainty, which is to assume that you do not assign probability at all to God’s existence. 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:
“That is very fine. Yes, I must wager; but I may perhaps wager too much.”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. (We have already mentioned ‘the true’ as one such thing; Pascal also seems to regard one’s worldly life as another.) In that case, the matrix is mistaken in presenting the two outcomes under ‘God does not exist’ as if they were the same, and we do not have a case of superdominance after all.
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.
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