Pascal’s Problem: A Mathematical Disproof of Pascal’s Wager

Guest Post This guest post comes from Chad DeVillier. He was raised Creationist/Christian, was very active in church, and attended bible college for a couple of years. He began questioning and eventually left the life of faith behind.
Pascal’s Wager (or Pascal’s Gambit) is stated in simple form thusly: It is better to bet on the existence of God because if you believe (B) and there is a god (G), your gain is +∞ (infinite reward), but if there isn’t a god (–G), your loss is –1 (inconsequentially small). If you don’t believe (–B) and there isn’t a god (–G), your gain is +1 (finite reward), but if there is a god (+G), your loss is –∞ (infinite punishment).
It can be expressed visually as follow:
image 1
The problem with Pascal’s Wager (the one I’m putting forth, anyway) is that it is one sided in its perspective. It was formulated within a Christian framework and, as with most ideas formulated in such a manner, it only takes into account the religious perspective.
The postulation states basically that belief in the specific deity yields infinite gain if true and finite loss if false, whereas disbelief in that deity yields infinite loss if true and finite gain if false. And from the selected monotheistic standpoint, this of course is true.
If your chosen deity exists, you lose one fleeting lifetime in pursuit of him (at the expense of your own autonomy) in order to gain blissful eternity by accepting him, rendering your lifetime on Earth unimportant in comparison. If one doesn’t believe in this deity, he or she loses out on said eternity because he or she wagered to win only one lifetime of pursuing his or her own brand of happiness. The choice, for the Christian, is clear.
But what if this were viewed from a non-religious context? Would the formula still look the same? I submit that no, it would not, and here’s why. Firstly, Blaise Pascal is allowing for two options and two alone—God or not God. He is ignoring the multitude of other gods, many of whom are expressly concerned with being the only god of choice. To choose one is to not only reject “not God” but to reject all the other gods fighting for your undivided allegiance.
The odds are now a very far cry from the 50/50 that Pascal initially proposed, because a bet in favor of any wrong god is a bet against the right one, and in addition to the thousands of known gods throughout history, the true god could yet be one that we have no knowledge of currently.
Secondly, a lifetime can only be understood as a finite gain or loss if your maximum understanding is infinity. But from the perspective of a nontheist, infinity is not on the table. The maximum span of a human’s existence is one lifetime, and therefore is the closest he or she can come to infinity.
Taking this perspective into account—with one lifetime being another infinity—the equation goes from this:
image 2
… to this:
image 3
The reason for this is simple: if there is no God, there is no infinite afterlife. The devout believer who is incorrect has not misspent one lifetime in the span of an eternity, they have misspent one lifetime when that is all there is and ever will be for them. A lifetime is their infinity, and the devout believer has spent it praying to either nothing or—random deity forbid—to the wrong god who is now disallowing them into the afterlife, bringing about either nonexistence or an afterlife of punishment.
In this last case, the net loss for the believer is infinitely negative. The formula above includes for such a contingent in the form of -∞. This allows for the parameters to be set by each specific possibility: in the maximum span of infinity, the infinite is infinite; in the maximum span of a lifetime, a lifetime is infinite.
One should notice that the above formula shows equal potential for gain or loss for both categories, the believer and the nonbeliever. If there are no other variables to take into account, there would be no perceivable benefit in either accepting the Christian god or rejecting him. Therefore, there is neither mathematical advantage nor disadvantage to disbelief.
It is important to note that, in matters of science, one must always begin with disbelief and only develop belief as facts emerge and are tested; one may indeed begin with an idea, but only an idea void of rigid belief since there exists at the onset no objective proof to form the basis of rigid belief. As the idea is tested, it is modified over time until it can be objectively seen as a credible and vindicated theory.
With mathematics unable to aid us in making a logical decision, the scientific mind must turn to other variables. Pascal’s Wager—while once explorative with probability theory and beneficial in the very inception of decision theory—is of no use here. It is antiquated and largely disproven, much like the religion it was intended to validate.

I have to confess that I now regard “the case for theism” as a fraud
and I can no longer take it seriously enough
to present it to a class as a respectable philosophical position—
no more than I could present intelligent design
as a legitimate biological theory.
— philosopher Keith Parsons,
on his leaving his profession