Blaise Pascal’s famous Wager proposes that prudence requires belief in God. Even if the probability of God’s existence is very small, the potential payoff—eternal salvation—is infinitely large, and so outweighs any finite cost of belief. On this reasoning, to “wager for God” is rationally mandatory.

This argument has long been criticized, but one of the most powerful challenges arises from what James Cargile (1966) called the possibility of “imagined gods.” The objection shows that the Wager, when taken seriously, collapses into incoherence.

The Oversimplified Partition #

Pascal presents the decision problem as if there are only two live hypotheses:

  1. The Catholic God exists.
  2. No God exists.

This framing, however, is inadequate. Theism is not a monolith. There are countless mutually exclusive conceptions of God or gods, each attaching infinite stakes to different conditions of belief and practice. To collapse them all into “the Catholic God” versus “not the Catholic God” misrepresents the logical space of possibilities.

Cargile’s Construction #

Cargile radicalizes the objection by showing how easy it is to generate infinite sets of mutually exclusive divine hypotheses. Consider the propositional function:

“For each real number $x$, there exists a God whose supreme delight is contemplating $x$, and who rewards or punishes us based on whether we share this devotion.”

Each such proposition is logically and epistemically possible, but they are mutually incompatible. If Pascal’s Wager requires us to assign a non-zero probability to “the Catholic God exists” on the grounds of mere possibility, then it requires us to do the same for each of these imagined gods as well.

This construction is not unique. We might equally suppose:

  • A God who saves only those who believe in exactly $n$ unicorns, for each $n \in \mathbb{N}$.
  • A God who saves only those who recite a particular finite string of words.
  • A God who rewards only those who affirm a given cosmological constant.

The point is not that these hypotheses are plausible, but that Pascal’s principle—treating any possible God as warranting a wager—renders them all relevant.

The Probability Problem #

Here the Wager meets its fatal difficulty. Expected value reasoning requires that probabilities be consistently assigned and sum to 1. But in the case of infinitely many imagined gods:

  • If each hypothesis is given non-zero probability $p$, then the total probability exceeds 1, which is impossible.
  • If each hypothesis is given probability 0, then the expected value of wagering is 0, since
  • If probabilities are distributed in an arbitrary or biased manner (say, privileging Catholicism), then the Wager loses its force as a general argument and simply presupposes what it aimed to establish.

Thus, the Wager’s mathematical machinery breaks down in the presence of infinitely many rival theistic hypotheses.

No Shortcuts Around Evidence #

The lesson of the imagined gods objection is that Pascal’s Wager cannot bypass evidential considerations. Once the space of possibilities is properly acknowledged, the Wager no longer compels us to believe in any particular God. Instead, it collapses into an indeterminate choice among infinitely many incompatible wagers.

The rational response, then, is not to bet blindly on one candidate but to return to the traditional epistemic task: weighing the actual evidence for and against specific religious claims.

Conclusion #

Pascal’s Wager remains a brilliant attempt to combine probability theory with existential decision-making. Yet, as Cargile and later critics have shown, its brilliance is also its weakness. Once probability is applied rigorously, the Wager dissolves. The imagined gods objection demonstrates that reasoning without evidence yields not a decisive mandate for belief, but a reductio ad absurdum.

In the end, the Wager does not compel faith—it compels us to recognize that no rational shortcut can replace the work of evaluating evidence.

References #

[1] Cargile, James. “Pascal’s Wager.” Philosophy, vol. 41, no. 157, 1966, pp. 250–57. JSTOR. Accessed 1 Sept. 2025.

[2] Mackie, J. L. The Miracle of Theism: Arguments for and against the Existence of God. Oxford University Press, 1982.

[3] Diderot, Denis. Pensées philosophiques. 1746.

[4] Hájek, Alan. “Pascal’s Wager.” The Stanford Encyclopedia of Philosophy (Fall 2021 Edition), Edward N. Zalta & Uri Nodelman (eds.). SEP. Accessed 1 Sept. 2025.