Pascal’s wager can be rewritten as:
(1) (Economically) rational behaviors are behaviors for which the potential cost multiplied by the probability of incurring this cost does not exceed the potential benefit multiplied by the probability of incurring this benefit.
(2) The potential benefit of belief in the God of the Christian worldview is eternal salvation, which is of infinite value.
(3) As it’s possible that the Christian worldview is true, the probability that it is is greater than zero, as possible entails a greater than zero probability.
(4) Infinity multiplied by any value greater than zero is infinity.
(5) No set of costs can exceed this potential benefit.
(6) Therefore belief in the Christian worldview and God is rational, disbelief is not (economically) rational.
The fallacious premise in Pascal’s argument, which becomes obvious when written out, is 3. There is an equivocation between two types of “possible,” potentially possible and actually possible. Actually possible refers to a probability of occurrence greater than zero. Potentially possible refers to the possibility of a probability of occurrence greater than zero. In this instance, it’s definitely potentially possible that the Christian worldview is true (as this possibility has not been ruled out). It is not, however, definitely actually possible. (We could live in a world where the Christian worldview is false and therefore the actual possibility of it being true is zero.) And as a result, the actual potential benefit of belief could be zero and the conclusion would not follow, given that cost/benefit estimates are based on actually possibilities, not potential possibilities.)
One could try to salvage Pascal’s argument by maintaining that the potential/actual distinction is irrelevant to cost/benefit analyses. And this argument would not be groundless. The rationality of cost/benefit analysis does not seem to be contingent on prior knowledge that a possibility is actual. Were it, few rational analyses could be made, as we live in a world were we don’t know if future alternatives are, in fact, actually possible. It’s potentially possible, after all, that our world is deterministic. And therefore that many of the possibilities that we see and evaluate are, in fact, not actually possible. To put this another way, if we grant the potential/actual distinction to avoid Pascal’s conclusion, an anti-Pascalian could make the same argument against the apparent rationality of all analyses for which the potential possible status is unknown, which is most.
Maintaining the irrelevancy of this distinction, though, allows for an absurd generalization of the argument. For example: as it’s potentially possible that standing on your head right now will result in eternal salvation, it follows that one should do so. Every act which is said to have an infinite cost/benefit would, if we ignore this distinction, be prescribed.
We are left with a quandary then. If knowledge of actual possibility is needed, then few analyses can be made. If knowledge is not needed, then reason dictates infinite absurdities. As a resolution, I would suggest that we make an implicit assessment of the probability that a potentially possibility is actual. In short, we assess the plausibility of the potential possibility. If we deem that a potential possibility is plausible we treat it as an actual possibility. But what about the belief in the Christian worldview? And what makes a potential possibility plausible, given that we don’t know the intrinsic status of it (i.e., whether it’s actually possible)? I would suggest for the latter, that a potential possibility is considered plausible if it meshes with the worldview that our minds have woven based on our experiences, direct and indirect. That standing our heads leads to eternal salvation isn’t plausible, for example, because it isn’t backed by a credence giving narrative. What about the Christian worldview? The plausibility of it, or any other, would seem to depend on the worldview from which you are approaching it. If you are approaching it from within, it likely would seem plausible. If not, it may or may not. If we deemed that it was plausible would Pascal’s conclusion follow? As with the potentially possible, the plausible, on closer inspection, is not the same as the actually probable. Between the two a logically insurmountable gulf lies. As a result, if we deem that the Christian worldview is plausible, Pascal’s conclusion would follow, but only insofar as any of the other conclusions, based on plausibility (instead of knowledge of actual probability), do. (Continued later).