The Jamesian Wager
A castaway builds a bonfire hoping to catch the attention of any ship or plane that might be passing nearby. Even with no evidence that a plane or ship is nearby, he still gathers driftwood and lights a fire, enhancing the possibility of rescue. The castaway’s reasoning is pragmatic. The benefit associated with fire building exceeds that of not building, and, clearly, no one questions the wisdom of the action.
Of course the castaway’s building of the fire does not require that the castaway believes that it will be seen. It requires only a belief that it might be seen. Now consider the question of God. What if there is no strong evidence that God exists? What if, that is, religious uncertainty obtains? Could one still believe, justifiably believe, that God exists? Or is belief when faced with religious uncertainty illegitimate and improper? Pragmatic arguments for theism are designed to motivate and support belief even in the absence of strong evidential support. These arguments seek to show that theistic belief is permissible, even if one lacks evidence that renders it likely that God exists. Theism is the proposition that God exists. God I understand as that individual, if any, who is omnipotent, omniscient, and morally perfect. A theist is anyone who believes that God exists.
Pragmatic arguments employ prudential reasons on behalf of their conclusions. A prudential reason for a proposition is a reason to think that believing that proposition would be beneficial. Other theistic arguments–the ontological proof or the cosmological argument for example–provide epistemic reasons in support of theism. An epistemic reason for a certain proposition is a reason to think that that proposition is true. Blaise Pascal (1623-1662) is famous, in part, for his contention that, if the evidence is inconclusive, one can properly consult prudence: “your reason suffers no more violence in choosing one rather than the other… but what about your happiness? Let us weigh the gain and the loss involved by Wagering that God exists.” According to Pascal, theistic belief, because of its prudential benefits, defeats its doxastic rivals of atheism and agnosticism. Pascal’s contention is encapsulated in what’s famously known as Pascal’s wager.
Pascal’s wager is the most prominent member of the family of pragmatic arguments in support of theism. Another prominent member of the family is found in the 1896 essay, “The Will to Believe,” authored by the American philosopher William James (1842-1910). James’s argument is concerned in large part with the immediate benefits of cultivating theistic belief, rather than any alleged benefit in the hereafter. This world is the primary concern, not the world to come.
It is the contention of what follows that one version of the wager–what we will call the “Jamesian wager”–provides good reason in support of theistic belief. The Jamesian wager contends that benefits associated with theistic belief hinge not just on a world to come, but also on this world. According to the Jamesian wager, theistic belief as such is beneficial, whether God exists or not. If the castaway’s fire provides warmth, and a means to cook, as well as a signal, then the castaway has all the more reason to build the fire.
Having an idea of the basic theory of decision-making greatly facilitates understanding pragmatic arguments. The theory of decision-making codifies the logic of rational action in situations in which one’s knowledge is limited. The usual limitation is a lack of a reliable basis on which to know or estimate the probabilities of various states of the world. In decision-making situations three elements are of importance: actions, states, and outcomes. Actions are the alternative ways of acting available to the deliberator: either wearing a coat or discarding it are two alternative actions. States are ways the world might be–it might be sunny or cloudy. Outcomes are the anticipated consequences or effects of each action if a particular state occurs–staying warm having worn my coat on a day that turns out chilly. A decision matrix usefully represents the relationships of these elements:
The outcomes will be arranged in cells, the number of which depends on the number of acts and states (2×2, or 2×3, or 3×3…). The cells are numbered sequentially from the upper left-hand cell across:
|State 1||State 2|
For simplicity’s sake, let’s stipulate that we’re concerned only with actions and states that are causally independent. One’s actions, that is, do not causally influence which state obtains. The deliberator values some outcomes; others she does not. “Utilities” is the term employed to represent the worth of the various outcomes for the deliberator. Some outcomes have a high value or utility for the deliberator, some a low or even negative utility (a disutility).
Probabilities, or the likelihood, of the various states play a large role in rational decision-making. If one knows the relevant probabilities (the risk involved), then a well-established rule is available: the Expectation rule. According to the Expectation rule, for any person S, and any number of actions available to S, if one of those actions has a greater expected utility than does the others, S should choose to perform that action. One calculates the expected utility of an act ψ by (i) multiplying the utility and probability of each outcome associated with ψ, (ii) subtracting any respective costs, and then (iii) summing the totals. So, for example, suppose one were deciding whether to carry an umbrella today. One prefers not to do so, but one also prefers even more not to get wet. We can use a 2×2 (two actions and two states) matrix to model these preferences, with the numbers within the cells representing the agent’s preference ranking of the various outcomes (the higher the number assigned to an outcome the greater the desire of the agent that the outcome obtains):
Suppose there is a 50% chance of rain today. The expected utility (EU) of carrying an umbrella is greater than that of not carrying, since:
½ (10) + ½ (2) = 6 = EU(carry)
½ (1) + ½ (5) = 3 = EU(do not carry)
This kind of decision-making or deliberation with knowledge (or estimation) of the relevant probabilities and utilities of the outcomes is what’s known as “decisions under risk.” Typically, decisions under risk employ objective evidence for estimating probabilities; even so, decisions under risk can employ subjective probabilities (probabilities that are degrees of belief or estimations of likelihood).
On the other hand, when deliberating with a knowledge of the outcomes but no knowledge of the probabilities associated with those outcomes, one faces a “decision under uncertainty” (sometimes called a “decision under ignorance”). No single rule governs decisions under uncertainty. Various rules are relevant depending upon one’s circumstances and preferences.
The Jamesian wager employs a decision-theoretic principle I call the “Next Best Thing Principle”:
D. Next Best Thing Principle: For any person S making a forced decision under uncertainty, if one of the actions, α, available to S has an outcome as good as the best outcomes of the other available actions, and never an outcome worse than the worst outcomes of the other actions, and, excluding the best outcomes and worse outcomes, has only outcomes better than the outcomes of the other actions, S should choose α.
This principle advises choosing an action whose middling outcomes are better than those of its competition, whenever the best outcomes and worse outcomes of the alternatives are equal in value. If a particular action has no outcome worse than the worst outcomes of the other alternatives, and has an outcome as good as the best outcomes of the others, and, moreover, in every other state has an outcome better than that of the others, then that action is rationally preferable.
There are, broadly speaking, two kinds of pragmatic arguments that have to do with belief formation. The first is an argument that recommends taking steps to believe a proposition because, if it should turn out to be true, the benefits gained from believing that proposition will be impressive. This first kind of pragmatic argument we can call a “truth-dependent” pragmatic argument, or more conveniently a “dependent-argument,” since the benefits are obtained only if the relevant state of affairs occurs. A prime example of a dependent-argument is Pascal’s best-known version of the wager: no matter how small the probability that God exists, as long as it is a positive, noninfinitesimal, probability, the expected utility of theistic belief exceeds the expected utility of disbelief because the reward for theistic belief is infinite if God exists. Recognizing the distinction between (A) having reason to believe a certain proposition is true, and (B) having reason to believe that proposition, it may be that taking steps to generate a belief in a certain proposition might be the rational thing to do, even if that proposition lacks strong evidential support. The benefits of believing a proposition can rationally take precedence over the evidential strength enjoyed by a contrary proposition; and so, given an infinite expected utility, Pascal’s wager contends that forming the belief that God exists is the rational thing to do, no matter how small the likelihood that God exists.
The second kind of pragmatic argument, which can be called a “truth-independent” pragmatic argument, or more conveniently, an “independent-argument,” is one which recommends taking steps to believe a certain proposition simply because of the benefits gained by believing it, whether or not the believed proposition is true. This is an argument that recommends belief cultivation because of the psychological, or moral, or religious, or social, or even the prudential benefits gained by virtue of believing it. In David Hume’s Dialogues Concerning Natural Religion, for example, Cleanthes employs an independent argument, “religion, however corrupted, is still better than no religion at all. The doctrine of a future state is so strong and necessary a security to morals that we never ought to abandon or neglect it.” Unlike independent pragmatic arguments, dependent ones are, in an important sense, truth-sensitive. Of course, being pragmatic arguments, dependent-arguments are not truth-sensitive in an evidential sense; nevertheless they are dependent on truth since the benefits are had only if the recommended belief is true. In contrast, independent pragmatic arguments, yielding benefits whether or not the recommended beliefs are true, are insensitive to truth. Independent-arguments, we might say, are belief-dependent and not truth-dependent. The Jamesian wager, as we will see, is an independent-argument, with the premise that theistic belief more likely generates a better life now than does nontheistic belief, whether or not God exists.
One interesting question regarding pragmatic arguments concerns their relation to the influential tradition of evidentialism. As a first stab we might understand evidentialism as asserting that:
EV. for all persons S and propositions p and times t, it is permissible for S to believe that p at t if and only if believing p is supported by S’s evidence at t.
The notion of support encapsulated in (EV) is that of a preponderance of evidence: a person may believe a proposition p just in case p is more likely than not on S’s evidence. Put more familiarly, (EV) asserts that one should believe a proposition only if it is supported by adequate evidence.
Endorsing principle (EV), many philosophers have held that pragmatic reasons for belief-formation are illegitimate since such reasons do not constitute adequate evidence for the truth of the belief. No doubt the best-known statement of the evidentialist imperative is that of W. K. Clifford (1845-79), “it is wrong always, everywhere, and for any one, to believe anything upon insufficient evidence.” Clifford presented (EV) in a moral sense: it is morally impermissible to believe anything that lacks adequate evidence. This understanding of (EV) might be called “ethical evidentialism.” The most plausible construction of ethical evidentialism builds on the claim that one should obey any rule that is such that, if everyone were to follow it, collective utility would be maximized. Since the baneful consequences of believing upon insufficient evidence are so great, this argument goes, there is a general duty not to subvert civilization by promoting credulity. One is obligated to follow (EV) because the pernicious consequences of everyone violating it are so great.
The normative force of (EV) can also be understood in an epistemic or intellectual sense: it is unreasonable to believe something without adequate evidence. This second understanding of (EV) is “cognitive evidentialism.” Here the idea is that a violation of (EV) is impermissible because doing so makes one unreasonable. Something like this is implied by Locke’s claim that “there are very few lovers of Truth for Truth’s sake… How a man may know whether he be so in earnest is worth enquiry: and I think there is one unerring mark of it–the not entertaining any proposition with greater assurance than the proofs it is built upon will warrant,” and in Hume’s dictum that “the wise man proportions his belief to the evidence.” The lack of sufficient evidence means, if Locke and Hume are correct, that the wise person lacks belief as well. Notice also that the dicta of Locke and Hume concern the strength of one’s belief. The idea here is that one’s degree of belief regarding a given proposition should be proportional to the probability of that proposition. This idea, along with the cognitive evidentialist understanding of (EV), is widespread in philosophy.
What is the stringency of the evidentialist imperative? Is it absolute or defeasible? Absolute evidentialism holds that there are no exceptions, every proposition falls under its purview. In either the ethical or cognitive sense, principle (EV) taken in the absolute sense consists of two normative claims: (E1) it is permissible to believe only propositions supported by sufficient evidence, and (E2) one’s degree of belief concerning a proposition ought to be proportional to the strength of the evidence enjoyed by that proposition. Claim (E1) supplies a lower bound on permissible belief; while (E2) renders the degree of belief, the strength of one’s believing, a function of the strength of the evidence. Taken together (E1) and (E2) imply that one ought to believe a proposition if it is supported by a preponderance of the evidence, whether propositional or experiential, and that one is permitted to believe a proposition only if it is supported by a preponderance of evidence.
Absolute evidentialism implies that if the evidence is balanced, or one finds oneself in a state of radical uncertainty, then one should neither believe, nor disbelieve. One should withhold belief. The only option open to one when the evidence is silent is to suspend belief. Understood in the absolutist sense, (EV) should be revised to read:
AE. for all persons S and propositions p and times t, S ought to believe that p at t if S’s evidence at t supports p; and S ought not believe that p if S’s evidence at t does not support p.
Defeasible evidentialism allows exceptions. Not every proposition falls under its purview, since it assigns the evidentialist imperative a limited scope, allowing the possibility that some propositions reside outside its jurisdiction. Defeasible evidentialism asserts that one ought to believe propositions supported by sufficient evidence, but it leaves open the possibility that one may have grounds other than the evidential from which to believe. Understood this way, (EV) would be revised to read:
DE. for all persons S and propositions p and times t, if S’s evidence at t supports p, then S ought to believe that p at t.
According to (DE), if the evidence is adequate, then the question is settled. If there is a preponderance of support for p, then one is required to believe p. Where the evidence definitely speaks, one must listen and obey. (DE) differs from (AE) in part since it says nothing about those occasions in which the evidence is silent, or is inadequate. If one assigns p a probability of one-half, then there is not a preponderance of evidence in support of p. (DE) says nothing about believing p in that case. Principle (AE), on the other hand, forbids believing p in that case.
While (AE) and (DE) are very attractive, neither passes muster, since there are occasions in which one has a moral duty to disbelieve a proposition that she takes to be well-supported. And since no one is irrational in doing her moral duty, it follows that there are occasions in which disbelieving a proposition that is well-supported is not only morally obligatory, but rationally permitted as well. Consider the following thought experiment. Suppose you were abducted by very powerful and very smart extraterrestrials that demonstrate their intent and power to destroy the Earth. Moreover, these fiendish ETs offer but one chance of salvation for humankind–you must disbelieve a proposition for which you have adequate evidence. You adroitly point out that you cannot, by a simple act of will, reject a proposition you have good reason to think is true. Devilish in their anticipation and in their technology, the ETs produce a device that can directly produce the requisite disbelief in willing subjects, a serum, say, or a supply of one-a-day disbelief-producing pills. It’s clear that you would do no wrong by swallowing a pill or injecting the serum, and, hence, bringing about and maintaining disbelief in a proposition for which you have adequate evidence, done to save humankind. If (AE) or (DE) were true, you’ve impermissibly dirtied your hands in the service of humankind, by violating a basic obligation. But that conclusion is too wildly implausible to take seriously.
To accommodate this development requires a revision of (EV):
EV*. for all persons S and propositions p and times t, if S’s evidence at t supports p, then S ought to believe that p at t, unless S has good reason to do otherwise.
Understood this way, evidentialism clearly has a prima facie status. (EV*) allows that one may be obligated to disbelieve or withhold belief from a proposition that in fact fits one’s evidence at a particular time.
For example, think of an Alpine hiker who, because of an avalanche and a blinding blizzard, is stranded on a desolate, mountain path facing a chasm. The hiker cannot return the way he came because of the avalanche, yet if he stays where he is, he will die of exposure as the temperature plummets. The hiker’s only real hope is to jump the chasm. Knowing that exertion generally follows belief the hiker realizes that his attempt will be half-hearted, diminishing his chance of survival, unless he brings himself to the belief that he can make the jump. But suppose the hiker takes himself to have strong evidence that he probably cannot make the jump. In circumstances like these, one is clearly justified in forming beliefs motivated by pragmatic reasons, since one’s best chance for survival depends on belief. The point of the Alpine hiker case is that pragmatic belief-formation is sometimes both morally and intellectually permissible.
This argument in support of the moral and rational permissibility of employing pragmatic reasons in belief-formation is an instance of what we might call the ‘basic argument‘ (or perhaps more precisely, the ‘basic argument scheme’):
A. Necessarily, no one is (overall) irrational in doing what he’s morally obligated to do. And,
B. it is possible that doing α is a moral obligation. Therefore,
C. it is possible that doing α is (overall) rational.
The ‘basic argument’ employs the alpha as just a placeholder for actions, or kinds of actions. The locution “(overall) rational” or “(overall) irrational” presupposes that there are various kinds of rationality, including moral rationality, epistemic rationality, and prudential rationality. The idea that there are various kinds of rationality recognizes that at any time one could have conflicting obligations. One might be obligated to do various things, doing all of which it’s not possible to do. Overall rationality is the all-things-considered perspective. It is what one ultimately should do; having taken into account the various obligations one is under at a particular time. Overall rationality, or all-things-considered rationality (ATC rationality), is one’s actual duty in the particular circumstances; even if one has other conflicting prima facie duties. The ‘basic argument’ can be formulated without presupposing that there are various kinds of rationality, by replacing the principle that no one is ever irrational in doing her moral duty, with the principle that moral obligations take precedence whenever a conflict of obligations occurs. In any case the ‘basic argument’ assumes that if in doing something one is not ATC irrational, then it follows that one is ATC rational in doing it. The relevance of the ‘basic argument’ is this. The action of forming and sustaining a belief upon pragmatic grounds can replace the placeholder. That is, pragmatic belief formation could be one’s moral duty. This is evident with the stranded Alpine hiker, whose only real chance of survival requires that he believe a claim for which he has little or no supporting evidence. If this is correct, then the chasm between the pragmatic and the permissible is, at times, bridgeable.
The Jamesian Wager
Consider the following decision matrix. Let “D” represent the existence of a nonstandard deity, a “deviant” deity, whether personal or impersonal. Such a deity is inclusivist in doling out the benefits of afterlife, rewarding not only its own devotees but also those who believe in no supernatural agency at all. Let “N” represent the world with no deity of any sort (call this state “naturalism”), and let “G” represent the god of theism.
Believe in G
Believe in Neither
Believe in D
With this matrix theistic belief is not obviously preferable, since infinite utility resides in columns G and D, and, the values of F3, F4, and F7, are presumably the same. This matrix illustrates the objection most frequently leveled against Pascalian wagers, what’s known as the “many gods objection.” According to this objection, the Pascalian is left with an embarrassment of riches, since one can construct a Pascalian wager for any number of deities, belief in which is incompatible with theistic belief.
Still all is not lost for the Pascalian. As long as F3 = F4 = F7 and the lower two cells of the D column are the same as the upper cell of the G column, the Pascalian can employ the N column as a principled way to adjudicate between believing theistically or not. That is, whether one believes theistically, or believes in a deviant deity, or refrains from believing in any deity at all, one is exposed to the same kind of risk (F3 or F4 or F7). The worst outcomes, that is, of theistic belief, of deviant belief, and of naturalistic belief are on a par. Moreover, whether one believes theistically, or believes in a deviant deity, or refrains from believing in any deity at all, one enjoys eligibility for the same kind of reward (8 = 8 = 8). The best outcomes, that is, of theistic belief, of deviant belief, and of naturalistic belief are on a par. But this “tie” can be broken in favor of theistic belief as long as we have reason to believe that the utility associated with F2 exceeds that of F5 and F8. Are there positive empirical benefits that correlate with theistic belief but not with belief in a deviant deity or belief in naturalism? To be sure there’s no reason to think that belief in a deviant deity correlates with positive empirical benefit, and especially when conjoined with the obvious opportunity costs associated with such a belief, there’s reason to think that F2 exceeds F8. Indeed, no matter how we might expand the matrix in order to accommodate the exotica of possible divinity, we would have reason to believe that F2 exceeds any this-world outcome associated with the exotica. So, the crucial question is: does the utility of F2 exceed that of F5?
If it does, then a Pascalian beachhead is established by employing the Next Best Thing Principle:
- For any person S making a forced decision under uncertainty, if one of the alternatives, α, available to S has an outcome as good as the best outcomes of the other available alternatives, and never an outcome worse than the worst outcomes of the other available alternatives, and, excluding the best outcomes and worse outcomes, has only outcomes better than the outcomes of the other available alternatives, then S should choose α. And,
- theistic belief has an outcome better than the other available alternatives if naturalism obtains. And,
- the best outcomes of theistic belief are as good as the best outcomes of the other available alternatives, and the worst outcomes of theistic belief are no worse than those of the other available alternatives. Therefore,
- one should believe in God.
Since (1) – (4) is strikingly similar to William James’ famous “Will-to-Believe” argument, let’s dub (1) – (4) the “Jamesian argument,” or the “Jamesian wager.” But is premise (2) true? Nicholas Rescher suggests it is not: “from every purely this-worldly point of view–material, social, and psychological–our interest is strongly engaged on the side of disbelief. As this world runs–to all appearances–every mundane advantage lies with disbelief.” On the other hand, William James thought the appearances ran the other way. In The Varieties of Religious Experience James suggests that religious belief produces certain psychological benefits:
A new zest which adds itself like a gift to life, and takes the form either of lyrical enchantment or of appeal to earnestness and heroism…. An assurance of safety and a temper of peace, and, in relation to others, a preponderance of loving affections.
If theism were true, we would expect theistic belief to be beneficial in this world as well as the next. But are there empirical benefits to believing? To seek an answer requires our leaving philosophy and venturing into the social sciences. The question–whether theistic belief is more beneficial than not believing–is very difficult and complex, in good part because of the variability involved. Since there is a significant body of social science literature reporting empirical measures of well-being and theistic religiosity at the individual level, two possible benefits seem worth investigating here: happiness and mortality (life span). To get a grip on this complex issue, let us stipulate that theistic belief provides more empirical benefit than not believing, even if no deity exists (a better “this-world” outcome), if, on average, believing theistically ranks higher than not believing theistically in at least one of the two categories of happiness and mortality, and is not lower in either of the two. Also, let us assume that happiness correlates with greater life satisfaction. What do the studies show? Two commentators (neither of whom could be called theistic apologists) characterize the relevant social science literature as “a huge, and growing literature that finds religion to be a reliable source of better mental and even physical health … regardless of the age, sex, race, ethnicity, nationality, or time period of the population being studied.”
With regard to happiness in particular, one researcher asserts “extensive studies have found the presence of religious beliefs and attitudes to be the best predictors of life satisfaction and a sense of well-being.” While this claim may be inflated, there is reason to think the correlation between religious belief and life satisfaction is significant. A study from the University of Minnesota of 3,300 parents of twins found a small but statistically significant correlation (.07) between religious commitment and happiness. More generally, a recent analysis of 100 studies, which examined the association of religious belief and life satisfaction, found that 80% of the studies reported at least one significant positive correlation between the variables. This analysis grouped studies as being either statistically significant in one direction, or in the other direction, or having no statistical significance at all, and then “counted votes.” With regard to happiness, there is sufficient evidence that believing theistically outranks not believing, at least slightly. This conclusion is no surprise, since it seems likely that theistic belief would generally produce a greater optimism among its adherents than would be found among nontheists. And, if optimism were a significant component of happiness, then we would expect the population with the greater incidence of optimism to also have a greater incidence of reported happiness.
The effect, if any, of theistic belief on mortality has been an object of study for well over a century. In 1872 Francis Galton, a cousin of Darwin, conducted a retrospective study of the life span of royalty, compared with others of similar economic status. Galton hypothesized that royalty have their length of life prayed for more often than do their economic peers, and yet there appeared to be no noticeable effect (“long live the Queen”). To no one’s surprise Galton’s methodology has not survived the test of time. A much more recent and sophisticated meta-analysis of 29 independent studies conducted in 2000, involving data from 125,000 subjects, found that “religious involvement had a significant and substantial association with increased survival.” In particular, frequent religious attendance (once a week or more) is associated with a 25-33% reduction in the rate of dying during follow-up periods ranging from 5 to 28 years. The increased survival rate associated with religious involvement was found to hold independent of possible confounders like age, sex, race, education and health status. This meta-analysis provides good reason to think that theistic belief provides a better this-world outcome with regard to mortality than does nonbelief. Of course, one might say that this result is not surprising given the evidence on happiness. If it is true that happiness is more frequently found among the religious, and if we expect happier people to generally live longer than unhappy people, then we would expect the mortality rates of the religious to be greater than those of the nonreligious. Still, until we have good evidence causally linking mortality rates with happiness rates, we can take the two as independent measures of empirical benefit.
Even a conservative reading of the evidence produced to date supports the judgment that believing in God is probably better for the individual than not believing with regard to happiness and mortality. As is the nature of social science, one’s judgment is subject to revision as new data are discovered. And, of course, the studies are population studies, so what is true on average may not hold in a particular case. Further, there is no obvious downside to these benefits. Or put another way, there seems to be no greater benefit generated by disbelief, which overcomes the advantages enjoyed by belief. So, even when these qualifications are noted, premise (2) of the Jamesian wager is more likely than not. Thus, the Pascalian has a sound escape from the many-gods objection, and we all have a means of navigation in the fog of religious uncertainty.
Continue the Debate
 Much of what follows is adapted from my book Pascal’s Wager: Pragmatic Arguments and Belief in God forthcoming from Oxford University Press.
 Some versions of the various theistic pragmatic arguments are intended to persuade even if it is extremely unlikely that God exists. I ignore that employment here.
 Pensées, translated by Honor Levi, (Oxford: Oxford University Press, 1995): 153-6.
 “The Will to Believe” in The Will To Believe and Other Essays in Popular Philosophy (1896; reprint, NY: Dover, 1956): 1-31.
 There are various proposed rules, some well-established, some not, for decisions under uncertainty. Informative introductions to decision theory include Michael Allingham, Choice Theory: A Very Short Introduction (Oxford: Oxford University Press, 2002); Ian Hacking, An Introduction to Probability and Inductive Logic (Cambridge: Cambridge University Press, 2001); and Michael Resnik, Choices: An Introduction to Decision Theory (Minneapolis, University of Minnesota Press, 1987).
 Dialogues Concerning Natural Religion, edited N. Kemp Smith (1779; reprint, Indianapolis: Bobbs-Merrill, 1947): 219.
 Lectures and Essays, Vol. II (London: Macmillan, 1879): 186.
 In other words, an indirect consequentialist formulation.
 An Essay Concerning Human Understanding (1689; rept., Oxford: Clarendon Press, 1975): 697.
 Enquiry Concerning Human Understanding (1748; rept., Oxford: Oxford University Press, 1982): 110.
 See for instance the important book Evidentialism: Essays in Epistemology by Earl Conee and Richard Feldman (Oxford: Clarendon Press, 2005). See also Bertrand Russell, Human Knowledge, Its Scope and Limits (NY: Simon & Schuster, 1948): 397-98; Brand Blanshard, Reason and Belief (London: Allen & Unwin, 1974): 400ff; Alan Gibbard, Wise Choices, Apt Feelings (Cambridge: Harvard University Press, 1990): 36-7; and Simon Blackburn, Truth: A Guide (Oxford: Oxford University Press, 2005): 3-22.
 I have adapted this example from William James. See his essays, “Is Life Worth Living?” 59; and see “The Sentiment of Rationality,” 96-7, both in The Will To Believe and Other Essays in Popular Philosophy.
 Nicholas Rescher, Pascal’s Wager: A Study of Practical Reasoning in Philosophical Theology (Notre Dame, IN: University of Notre Dame Press, 1985): 31.
 The Varieties of Religious Experience (1902; rept. NY: Modern Library, 1936): 475-6.
 Rodney Stark and Roger Fink, Acts of Faith: Explaining the Human Side of Religion (Berkley, CA: University of California Press, 2000): 31-2. See also Harold Koenig, Michael McCullough, and David Larson, Handbook of Religion and Health (Oxford: Oxford University Press, 2001): 394.
 Quoted in Ralph W. Hood, Jr., Bernard Spilka, Bruce Hunsberger, and Richard Gorsuch, The Psychology of Religion (NY: Guilford Press, 1996, 2nd ed.): 384.
 David Lykken, Happiness (NY: St. Martin’s Press, 1999): 18-9.
 Koenig, McCullough, and Larson, Handbook of Religion and Health, 117, 215-5.
 Francis Galton, “Statistical Enquires into the Efficacy of Prayer” The Fortnightly Review 12 (August, 1872): 125-35.
 Koenig, McCullough, and Larson, Handbook of Religion and Health, 328-30. For detail on the meta-analysis, see M.E. Cullough, W.T. Hoyt, D. Larsen, H.G. Koenig, and C. E. Thoresen, “Religious Involvement and Mortality: A Meta-analytic Review.” Health Psychology 19 (2000): 211-22.
 See also the interesting report on religiosity and mortality and morbidity rates in Jeffrey S. Levin, “How Religion Influences Morbidity and Health” Social Science and Medicine 43/5 (1996): 850. For a contrary view, see W. Matthews, et al. “God’s HMO: Prayer, Faith, Belief & Physical Well-being,” Skeptic Magazine 8/2 (2000): 68.
 One might object that perhaps there is a similar empirical benefit to be had with non-Western religions; we just lack the studies to know this. And if so, the set of Pascalian approved choices once again inflates. The problem with this objection is that it ignores that we are discussing a forced issue.
Copyright ©2008 Jeffrey Jordan. The electronic version is copyright ©2008 by Internet Infidels, Inc. with the written permission of Jeffrey Jordan. All rights reserved.