2.1 Explaining the Epistemic Wager

Consider the following decision matrix, which represents the epistemic wager (table 2):

Table 2 The Epistemic Wager

In table 2, U represents the value of the epistemic goods associated with going to heaven. Notice that those who believe in God receive U, unless God does not exist, but those who do not believe in God receive U only if universalism is true and everyone goes to heaven (but, on this outcome, they are dinged for having a false belief). V is the value of the epistemic goods associated with going to hell. There may be some epistemic goods associated with hell, assuming people in hell learn things. Nonetheless, I argue that U is greater than V. Also, as I discuss below, U and V may be infinite or finite.

F1, F2, F3, and F4 are all finite. F2 and F3, while similar, have different values because theistic beliefs have different truth values on each outcome. F4 represents the badness of having a false theistic belief during one's pre-afterlife existence; its value may be negligibly small.Footnote ³ P1–P4 are probabilities. P1 is the probability of [theism and the traditional view of hell], P2 is the probability of [theism and the annihilationist view of hell, that is, that nonbelievers cease to exist after death], and P3 is the probability of [theism and universalism, that is, that all go to heaven]. P4 is the probability of atheism.

This table assumes a couple things. First, given theism, there are three possible afterlives for nonbelievers that are mutually exclusive and exhaustive. If we understand these afterlives broadly—that is, heaven represents the net good afterlives, hell represents the net bad afterlives, and annihilationism represents the net neutral afterlives—it is plausible that they exhaust the probability space. Second, for the argument to work, the disjunction of P2 or P3—that is, either annihilationism or the traditional view of hell—must be (at least) non-zero and non-infinitesimal. Note that this is consistent with thinking universalism is quite likely, and even with believing universalism, as long as one does not assign universalism credence 1. On certain finite versions of the epistemic wager, this assumption may need to be slightly stronger, but it is in most cases consistent with believing universalism.

The argument requires that either (1) the value of P2, the probability of annihilationism, is sufficiently high; or (2) U > V, that is, it is epistemically better to be in heaven than to be in hell. On most credence functions, the value of P2 will be high enough for the argument to go through, but there are also good reasons to think that (2) holds—that U is in fact greater than V. Here are a few. Consider the beatific vision—the doctrine that those in heaven are face to face with God and see God's essence. This is commonly understood to have an intellectual component, where one gains new beliefs, knowledge, or understanding about God, themselves, and the world in an indescribably rich and glorious way (Aquinas Reference Aquinas1265–1274; Boersma Reference Boersma2018). Further, on many theological traditions, those in heaven have direct access to God. They can ask God any question, about any topic that they want. Not only is this objectively epistemically valuable on almost any theory of epistemic value—one has access to unlimited true beliefs, knowledge, accurate credences, understanding, and the like—but it is also an epistemic good that is likely to be desirable to many. Thus, it is also valuable if epistemic norms are instrumental, derived from the one's epistemic goals. One can learn any piece of information by simply asking God about it.

Further, while it is possible that people in hell learn things, and potentially even attain significant knowledge, if hell is in other ways undesirable, unpleasant, or involves serious suffering, people there are less likely to pursue epistemic goods. There is also the possibility that hell is epistemically bad because it is a place of confusion and self-deception; those in hell may actually gain false, unjustified, or incoherent beliefs. Thus, hell may have an overall negative epistemic value. Finally, recall that V is the epistemic value of not believing in God if God exists. Those who do not believe in God thus miss out on at least one true belief (but potentially more, as they are also likely to miss out on true beliefs that follow from or cohere with theism).

This raises an important, related question: whether U (and V) are infinite or finite. Is afterlife infinitely epistemically good? Suppose those in heaven gain a finite number of epistemically valuable states per day (or per finite period) for all eternity. On a synchronic measure of epistemic value, then, heaven is infinitely epistemically valuable.Footnote ⁴ If one also has epistemically valuable states for an infinite time period, then heaven is also infinitely epistemically good on a diachronic measure of epistemic value. I do not completely rule out the possibility that hell is infinitely epistemically valuable for similar reasons, even though I gave some reasons to doubt this above. If heaven and hell are both infinitely good, but heaven is better, then to compare them, we need a decision theory that enables the comparison of different sizes or kinds of infinities.

Not all infinite epistemic goods are decision-theoretically equal. For example, getting one hundred pieces of new knowledge a day is better than getting one per day, which is better than getting one every thousand years, even though these are all, strictly speaking, infinite. Further, if the content of what is learned matters, then we should prefer gaining a significant piece of knowledge every day to gaining an insignificant piece of knowledge every day. Finally, we should prefer a 99 percent chance at getting an infinite epistemic good than a 1 percent chance at the same good, so both utility and probability matter in the infinite case. (Plausibly, we can use ordinally ranked infinities to compare these cases.)

The lesson—that we should not treat all infinities the same in decision theory—is one that many have drawn in response to the mixed strategies objection to the traditional wager, and there are numerous formal models to compare infinities that can easily be translated over to the epistemic wager. These models utilize mathematical tools such as limits and ratios or surreal numbers (see, for instance, Bartha Reference Bartha2007; Jackson and Rogers Reference Jackson and Rogers2019; Chen and Rubio Reference Chen and Rubio2020). The epistemic wager is consistent with a variety of formalisms; we need not commit to a specific way to compare infinities here, as they agree on the main results we need. On all of these models, given an infinite version of the wager, the value of F1 and F2 and the probability of [hell or annihilationism] will not matter, as long as the probability of [hell or annihilationism] is non-zero and non-infinitesimal.

Nonetheless, some are skeptical of infinities in general—or at least skeptical of the use of infinities in decision theory. Others might simply question whether the epistemic gains in the afterlife are infinitely valuable. To account for this, we can utilize an alternative model on which U and V are finite but nonetheless quite large. On the finite version of the wager, the probability of the disjunction of P2 or P3—annihilationism or the traditional view of hell—would need to be larger than simply non-zero/non-infinitesimal. However, we can utilize arbitrarily large finite values for U and V, so that the probability of the disjunction of P2 and P3 can be extremely small. Thus, the epistemic wager is consistent with afterlife epistemic goods being either finite or infinite.

Finally, for the epistemic wager to be successful, one needs to care about promoting long-term expected epistemic value (in a synchronic or diachronic sense). As with the traditional wager, if one is an epistemic future discounter, then, depending on the exact discount function, the epistemic wager may not have purchase. Some of the above epistemic consequentialist views described above (such as some versions of epistemic utility theory) focus only on the short-term epistemic consequences of, for example, adopting a certain credal state. Thus, not all versions of epistemic consequentialism pay attention to long-term consequences (for example, Joyce Reference Joyce1998).Footnote ⁵ But these restricted views face other challenges. When should we stop caring about the epistemic consequences? Is there a non-ad hoc way to determine the cut-off point? Second, most philosophers think discounting in the practical case is irrational; why would it be rational in the epistemic case? (See Jackson and Rogers Reference Jackson and Rogers2019: 79–82.) Finally, as I argue below, if one does not consider total consequences of one's decisions when acting, it is not clear that one is following a consequentialist norm.

In sum, the epistemic wager requires three things: (1) a sufficient probability of [annihilationism or the traditional view of hell]—but this probability can nonetheless be extraordinarily low (how low depends on whether the wager is finite or infinite); (2) either (a) a sufficiently high probability of annihilationism (but again, this can still be relatively low), or (b) that the epistemic value of heaven is greater than that of hell; and (3) long-term expected epistemic consequences to be normatively relevant.

2.2 The Traditional Wager Verses the Epistemic Wager

There are at least four salient differences between the traditional wager and the epistemic wager, several of which are clear benefits of the epistemic wager.

The first difference involves the irrationality objection to the traditional wager. According to this objection, beliefs formed for practical reasons are epistemically irrational. If I believe p because you have paid me money to believe p, or simply because I want p to be true, my belief is not epistemically rational. Beliefs formed on the basis of the traditional wager are similarly based on practical reasons, and thus—so the objection goes—also epistemically irrational. This general line of reasoning is advocated by several in the literature, including Clifford (Reference Clifford1877: 289); Flew (Reference Flew1976: 64); Mackie (Reference Mackie1982: 202); Oppy (Reference Oppy1991: 167); Schroeder (Reference Schroeder2012: 266). (For responses to the irrationality objection, see Jackson Reference Jackson2016; Benton Reference Benton, Benton, Hawthorne and Rabinowitz2018, Jackson and Rogers Reference Jackson and Rogers2019; Jackson Reference Jackson, Fuqua, Greco and McNabb2023c; Jackson Reference Jackson2023a.)

But this objection does not apply to the epistemic wager. If, as assumed, epistemic consequentialism is the correct theory of epistemic normativity, then the epistemic wager provides an epistemic reason to believe in God, not just a practical reason. Belief in God maximizes expected epistemic value, as it promotes epistemically valuable states and helps us avoid epistemically invaluable states. One of the most important features of the epistemic wager is that it provides epistemic, rather than practical, reasons for belief. Against the backdrop of epistemic consequentialism, the irrationality objection does not apply.

To drive this point home, consider an analogy. For a long time, probabilism, the view that one's credences should be probabilistically coherent, was taken to be justified by Dutch book arguments: one could lose money in a series of bets if they had incoherent credences. However, this view faces a key objection: this a pragmatic reason to have probabilistic credences, not an epistemic one. In response, the new accuracy arguments for probabilism use epistemic decision theory to show that for all non-probabilistic credences, some probabilistic credences are guaranteed to be more accurate (Joyce Reference Joyce1998). Thus, one of the major applications of epistemic decision theory is that it provides a non-pragmatic justification of probabilism. This gives us an epistemic reason to have coherent credences. Along similar lines, the epistemic wager provides an epistemic reason for belief in God, rather than merely a pragmatic one.

Consider a second way the epistemic wager differs from the traditional wager. Another worry for Pascal's wager involves the motives exemplified by taking the traditional wager. The thought is that if one simply believes in God to avoid hell or get the reward of heaven, this seems unvirtuous—something that God would not be pleased with. While I am not convinced this objection is correct (see Jackson Reference Jackson2023b), those sympathetic to this worry may prefer the epistemic wager. Consider the person who wagers on God because they take it to be their best shot of getting at the truth. Being motivated by epistemic goods, such as gaining knowledge or finding answers to significant questions, is admirable. Thus, the motives involved in the epistemic wager may be more virtuous than those involved in the traditional wager.

Third, the traditional wager is often viewed as a simple trumping argument. Infinite value is always better than finite value, so one should wager on God, even if their credence in theism is extraordinarily low. The epistemic wager is more complex, partially because it is not obvious that the epistemic value is heaven is infinitely better than that of hell. Thus, the epistemic wager does not involve the simple trumping of the traditional wager. However, several authors have argued that even the traditional wager cannot rely on simple trumping principles, due to the mixed strategies objection (see Duff Reference Duff1986; Hájek Reference Hájek2003; Jackson and Rogers Reference Jackson and Rogers2019; Chen and Rubio Reference Chen and Rubio2020). This may be a feature of all plausible versions of Pascal's wager.

The fourth and final difference is that the epistemic wager does better the higher one's credence that non-believers are annihilated, whereas the traditional wager does better the higher one's credence that nonbelievers go to hell (unless hell has negative epistemic value). This is because hell may be epistemically better than being annihilated, but is pragmatically worse. Epistemically and pragmatically, annihilation has utility 0. By contrast, going to hell has a negative pragmatic utility, but may have a positive epistemic utility.

3.1 Belief and Control

One might object that, given the epistemic wager, I cannot simply make myself believe in God, even if I know that doing so will lead to a lot of epistemic goods down the line. In this, the epistemic wager faces a control problem: believing for long-term epistemic goods seems just as difficult as believing for practical reasons. In reply, I merely argue above that we epistemically ought to believe in God, and I argue for this only conditionally, on the supposition of epistemic consequentialism. I have not even argued that the antecedent holds, much less argued for anything about control over belief.

The objector might reply that the epistemic ought implies can. In other words, if S epistemically ought to phi, then S can phi. Given this principle, if we cannot control our beliefs, one can reject my claim that we should believe in God via modus tollens reasoning. I have two preliminary replies. First, again, this is not an objection to the conditional claim, which is my primary thesis. And second, many (Feldman Reference Feldman2000, Hieronymi Reference Hieronymi2009, McHugh Reference McHugh2012) deny that epistemic ought implies can, so epistemic obligations can govern our beliefs even if we cannot control them.

That said, this argument would be less interesting if the antecedent and the consequent of the conditional thesis were false, and I do not want the argument to hang on whether epistemic ought implies can. This brings me to a third reply, which focuses on the acts in the epistemic decision matrix. Suppose first that the acts are as they are in the matrix above, simply believing and not believing in theism. One interesting thing about the epistemic wager is that there is less pressure to move away from this straightforward interpretation, since it provides epistemic reasons, and those apply to belief. On the straightforward interpretation, we either need to deny that ought implies can or argue that we can control beliefs. I argue elsewhere (Jackson Reference Jackson2023a) that when it comes to belief in God, many of us are in an epistemically permissive case: our evidence underdetermines what we epistemically ought to believe. I also argue that, in permissive cases, we have a much more direct kind of control than in other cases. I argue that we have either direct or what I call “semi-direct” control over belief in permissive cases, and thus we can, in some meaningful sense, choose to believe based on Pascalian considerations. Further, almost everyone who works on issues about belief and control agrees that we have indirect doxastic control: we can try to believe certain things, and, in many cases, successfully influence our beliefs over time. This is even more plausible when we consider propositions that are candidates for being permissive (like God exists) rather than propositions that are clearly true or false, like 1+1=2 or the Earth is flat.

Nonetheless, I am also open to interpreting the acts in the epistemic wager more broadly. We might frame the wager in terms of things besides belief, such as desire or action. Alternatively, the wager might be understood not in terms of belief but in terms of faith (assuming faith does not entail belief, as contended by Pojman Reference Pojman1986; Audi Reference Audi1991; Alston Reference Alston, Jordan and Howard-Snyder1996, among others). Or the act in question might be a commitment to God, a commitment to pursue a relationship with God, or a commitment to accept (that is, act as if) God exists (see Golding Reference Golding1994; Jones Reference Jones1998; Rota Reference Rota2016a, Reference Rota2016b). While this requires that there are epistemic reasons for action—which is controversial; see Simion (Reference Simion2018)—this is another viable version of the epistemic wager.

There are thus at least three ways out of this objection to the epistemic wager. One, we frame the epistemic wager about believing or trying to believe, and argue that we have the relevant kind of control, even if indirect. Two, we deny that epistemic ought implies can, or three, we focus on epistemic reasons for action or commitment.

3.2 Trade-Offs and Long-Term Consequences

According to the epistemic wager, it is epistemically rational to believe in God because it leads to a large expected epistemic benefit. However, one might argue that leading to a bunch of other true or rational beliefs about q and r cannot make my belief that p epistemically rational; this is what Berker (Reference Berker2013a) calls ‘the separateness of propositions’. In other words, simply because believing in God will lead to a bunch of expected epistemic value down the line does not make my belief in God epistemically rational, especially if that value concerns other propositions.

In reply, first note that the trade-off worry is an objection to epistemic consequentialism, which I am not arguing for. This objection parallels a classic objection to ethical consequentialism, namely, that ethical consequentialism does not respect the separateness of persons (but in the epistemic case, it is the separateness of propositions). Of course, what one's view says about this case depends on their epistemic axiology. However, many epistemic consequentialists do not merely value the accuracy of a single attitude, but the accuracy of a belief or credal state as a whole.

And it is hard to see how one could have a genuine version of epistemic consequentialism without committing to the permissibility of some epistemic trade-offs. Littlejohn (Reference Littlejohn, Ahlstrom-Vij and Dunn2018) and Wedgwood (Reference Wedgwood, Ahlstrom-Vij and Dunn2018) both emphasize that, in a genuine consequentialist theory, the total consequences must be used to derive the normative property. As Ahlstrom-Vij and Dunn (Reference Dunn, Ahlstrom-Vij, Ahlstrom-Vij and Dunn2018: 6) point out, if all that matters for the thing being evaluated is just the thing itself, it is not clear how this is a version of consequentialism. On most versions of consequentialism, we do not restrict the relevant consequences, as long as they concern things in our value theory. And being concerned only with one's attitude toward a single proposition does not seem like a sensible epistemic value theory.

Further, if I am right that many of us are in an epistemically permissive case with respect to theism, so that we could be rational as theists, atheists, or agnostics, then it is plausible that downstream epistemic goods could be a tiebreaker. If multiple attitudes to p are evidentially on a par, then one could consider other epistemic consequences that go beyond one's attitude toward p. To consider an analogy from the ethical case, consider the choice between two actions: action 1 saves only S's life, and action 2 saves S's life and a bunch of other lives. Even if S has special axiological consideration, action 2 seems better, as it dominates action 1.

Finally, note that the epistemic wager may be successful apart from a full-blown commitment to epistemic consequentialism. There are at least two possibilities. First, one might endorse epistemic consequentialism with side constraints. Maybe one should believe the thing that has the best epistemic consequences unless their evidence suggests it is definitely or very likely false. For example, believe that God exists because of the large expected epistemic value, unless your credence that God exists falls below some threshold. This would avoid the consequence that S's believing p can be epistemically rational even if, say, S thinks p is obviously false; S's epistemic position toward p must be sufficiently favorable. (Relatedly, Michael Rota [2016b] defends a version of the wager on which one should wager if their credence in theism is at least 0.5. The threshold need not be that high, however.)Footnote ⁶

Second, there are deontological views in ethics on which one ought not to commit certain acts unless the consequences are extreme. For example, one might think torture is wrong unless, for example, a million lives are at stake. One could adopt a similar view in epistemology: epistemic consequences do not matter for rationality unless the relevant consequences are sufficiently weighty. When the stakes are quite high, however, epistemic rationality depends on consequences. Because there is so much to gain in the epistemic wager, we ought to believe in God, even if the consequences are not relevant when the epistemic stakes are lower (compare: we should not torture someone to save three lives).Footnote ⁷

3.3 Many Gods

One might wonder what the epistemic wager implies about mutually exclusive religions. Suppose I take the epistemic wager and believe in the God of religion 1; I may not get the epistemic goods of religion 2.

My response is twofold. First, it is sensible to simply ask the question of whether one ought to be a theist, and then leave the choice between religions for later. The main purpose of this essay is not to adjudicate between religions, but to draw a connection between general theism and epistemic consequentialism.

Second, if all religions offer roughly the same epistemic goods, then according to the epistemic wager, one should practice the religion that one thinks is most likely to be true. It is not obvious, however, that we should quantify the epistemic value of all religions equally; the epistemic goods to be gained in the afterlife vary widely by religious tradition. For example, as discussed above, on many versions of Christianity, heaven involves the beatific vision—seeing God's essence and gaining a complete understanding of the world. Alternatively, by practicing certain versions of Buddhism, one can eventually reach enlightenment, the state of comprehending reality as it is (see Wright Reference Wright2016), which also seems quite epistemically valuable. Mormonism teaches that humans can eventually become divine, as they ‘progress toward perfection and ultimately realize their divine destiny as heirs of eternal life’ (Church of Jesus Christ of the Latter-Day Saints 1995). The epistemic benefits of being divine seem quite significant, to say the least. Thus, various religions at least offer different epistemic goods; there is a further question of how to weigh these goods against each other. If one thinks that a certain religion offers better epistemic goods than another, one can also factor that into the decision table; if one takes the goods of various religions to be infinite, one can utilize one of the decision-theoretic methods for comparing infinities discussed above. A detailed theological comparison of the epistemic goods of various religions is a promising area of further research.Footnote ⁸ (For more on using the wager to compare religions, see Jackson and Rogers Reference Jackson and Rogers2019.)

3.4 Hell versus Annihilationism

Above, I suggest that hell may, in some sense, be better than annihilationism. One may wonder: Is this right? This seems to have counterintuitive consequences. For instance, if we take heaven out of the picture, then, from an epistemic perspective, I should maximize my chance of going to hell.

In reply, there are two views of hell relevant for this objection. On the first, hell is genuinely epistemically better than annihilationism. Nonetheless, this does not mean that one should all-things-considered prefer hell—hell is merely better from an epistemic point of view. To decide what one should all-things-considered prefer, one may need to weigh epistemic and practical goods against each other. (This is also potentially relevant to the many-gods issue, because there is also the possibility that one religion's afterlife is epistemically better, and another's is practically better. This would also require weighing different types of goods against each other.) Second, as mentioned above, there is also the possibility that hell is a place of self-deception and confusion. On this picture, the epistemic wager looks more like the traditional wager—hell has a negative epistemic value. Then one should prefer annihilation to hell.