Pascal's Wager and Pragmatic Arguments for Belief

The Wager / Pragmatic Case

Abstract

Blaise Pascal and William James agree on the decisive point against strict evidentialism: where reason cannot settle a question that we are nonetheless forced to decide, the benefits of believing can rationally govern the decision. Pascal builds a truth-dependent argument — the infinite reward is had only if God exists — driven by expected-utility maximization under uncertainty. James builds a truth-independent argument — some goods of belief accrue "even now" — driven by the claim that a rule forbidding belief wherever evidence is silent would itself irrationally cut us off from certain truths. Together they constitute the pragmatic case: theistic belief is rational not because it is proven but because, under genuine uncertainty, it is the best bet.

Formal statement

Pascal (the Argument from Generalized Expectation): as in the formal statement above — positive probability, one infinite payoff, expected-utility maximization, therefore wager for God (SEP Pascal's Wager §4).

James (the Will to Believe): reconstructed from the SEP's summary (SEP Pragmatic Arguments §3):

1. The decision whether to accept theism is a genuine option — living, momentous, and forced.
2. Theism is intellectually open — the evidence does not conclusively decide it.
3. There are vital goods at stake in accepting theism.
4. No one is irrational or immoral in risking error for a chance at truth and a vital good.
5. Therefore one may accept theism.

Key evidence / textual basis

Pascal's text supplies every premise directly. The forced option: "you must wager. It is not optional. You are embarked" (Pascal, Pensées fr. 233). Reason's silence: "'God is, or He is not.' But to which side shall we incline? Reason can decide nothing here. There is an infinite chaos which separated us" (Pascal, Pensées fr. 233). The dominance intuition of the first wager: "If you gain, you gain all; if you lose, you lose nothing. Wager, then, without hesitation that He is" (Pascal, Pensées fr. 233). The generalized expectation, where the probability drops out: "there is here an infinity of an infinitely happy life to gain, a chance of gain against a finite number of chances of loss, and what you stake is finite... you must give all" (Pascal, Pensées fr. 233). And the decision-theoretic maxim in Pascal's own words: "every player stakes a certainty to gain an uncertainty... the uncertainty of the gain is proportioned to the certainty of the stake according to the proportion of the chances of gain and loss," from which "our proposition is of infinite force" (Pascal, Pensées fr. 233). Ian Hacking accordingly calls the Wager "the first well-understood contribution to decision theory" (SEP Pascal's Wager §1).

Crucially, Pascal answers the objection that belief cannot be willed. To the interlocutor "I am so made that I cannot believe. What, then, would you have me do?" he prescribes action ahead of assent: convince yourself "not by increase of proofs of God, but by the abatement of your passions," following those who "began; by acting as if they believed, taking the holy water, having masses said, etc." — and "Even this will naturally make you believe" (Pascal, Pensées fr. 233). This is the psychology-of-belief claim on which the whole prudential strategy rests: belief is cultivable through habituated action. The SEP glosses this as indirect control — pragmatic belief-formation "neither entails nor presupposes Doxastic Voluntarism," only "indirect, or roundabout, control over belief-formation" via accepting a proposition and then acting on it (SEP Pragmatic Arguments §8).

James supplies the complementary, truth-independent engine. His foil is Clifford, and his master claim is epistemological: "a rule of thinking which would absolutely prevent me from acknowledging certain kinds of truth if those kinds of truth were really there, would be an irrational rule" (SEP Pragmatic Arguments §3). His decisive examples are dependent and restricted truths — social cooperation, friendship, and (if theism is true) religious goods — whose evidence is available only to those who first venture belief: cases "where a fact cannot come at all unless a preliminary faith exists in its coming" (SEP Pragmatic Arguments §3). Tellingly, James endorsed the Wager: he judged that with a genuine option in place, "Pascal's argument, instead of being powerless, then seems a regular clincher" (SEP Pragmatic Arguments §3).

Leading proponents

• Blaise Pascal — Pensées (1670), fr. 233 Brunschvicg (the "Infinite—nothing" fragment): the four wagers, the forced option, expected-utility maximization, and the holy-water psychology of belief. In corpus; quoted directly. Note the SEP-life caution that Pascal wrote as "someone who already believed," so a probability calculation is "logically posterior to belief" and shows only "that those who have accepted divine grace... have made a wager that is not unreasonable" (SEP Pascal (life) §2).
• William James — "The Will to Believe" (1896): the genuine-option framing, dependent and restricted truths, and the truth-independent case that belief can be permissible where evidence is silent (corpus gap: essay not in raw/; via SEP Pragmatic Arguments §3).
• J. S. Mill's "license to hope" and the consolation/needs arguments (Beattie, Newman) form the surrounding family — hope, not belief, may exceed the evidence, since "the standards for the permissibility" of belief "are considerably higher" (SEP Pragmatic Arguments §4).

Strongest counter-arguments

The pragmatic case must answer three families of objection, developed at full strength in the next view: (i) the many-gods objection, that the table needs more columns, since "one could formulate a Pascalian Wager for Islam" or countless other deities (SEP Pragmatic Arguments §2); (ii) the moral objections, that believing for reward corrupts the believer and that the divine plan the Wager presupposes is itself unjust (SEP Pascal's Wager §5.5); and (iii) the infinite-utility and validity objections, that infinite utilities are incoherent and that mixed strategies tie the Wager's expectation (SEP Pascal's Wager §5.1, §5.4). Against James specifically, the charge is that his rule "constitutes an unrestricted license for wishful thinking" (SEP Pragmatic Arguments §3).

Responses

Pascal and James have principled replies. To wishful thinking, James restricts permissible passional belief to options that are genuine and intellectually open: where "there's a preponderance of evidence" a "commitment to abide by the evidence is triggered," so his rule licenses belief only where evidence is genuinely silent (SEP Pragmatic Arguments §3). To the voluntarism worry, Pascal never claims belief is willed directly; the holy-water regimen is precisely a technology of indirect control (SEP Pragmatic Arguments §8). The many-gods and moral objections are the ones that force the refinement treated in the third view. The infinite-utility objection is the deepest, and where the Wager's defenders have done the most technical work.

Assessment

Assessment: Live — the pragmatic case is philosophically serious and, in James's hands, survives the wishful-thinking charge by restricting itself to genuine, evidentially open options; Pascal's decision-theoretic core is formally valid on his own premises (as even Mackie and Hacking concede) and its psychology of indirect belief-formation is defensible. What remains contested — and drives the third view — is whether the premises themselves survive the many-gods and infinite-utility objections (SEP Pascal's Wager §5.4).

The Standard Objections

Abstract

The critics do not typically deny that Pascal's argument is valid; several concede it is (J. L. Mackie among them). They attack the premises and, more sharply, the moral propriety of the whole enterprise. W. K. Clifford supplies the ethics-of-belief objection: believing on insufficient evidence is not merely unwise but wrong, a corruption of the self and a danger to society. J. L. Mackie and others press the many-gods objection (the decision table is under-specified), the infinite-utility objection (the notion is incoherent or admits too many infinities), and the mixed-strategies objection (any action ties the Wager's expectation). These are the reasons most philosophers regard the Wager as, at best, in need of heavy repair.

Formal statement

The objections, as catalogued by the SEP (SEP Pascal's Wager §5):

1. Many-gods (premise 1, more columns): reason "can decide nothing here," so rival theistic hypotheses are equally live; by parallel reasoning the Wager "proves too much."
2. Infinite-utility incoherence (premise 1, the payoff): the very notion of infinite utility is suspect, or the table should contain several infinities (a forgiving God rewarding all; negative infinity for wagering against).
3. Undefined or zero probability (premise 2): a strict atheist may rationally assign p = 0, whereupon ∞ × 0 = 0 and the Wager has no pull.
4. Invalidity via mixed strategies (the inference): strategies other than outright wagering — "toss a coin; heads, wager for God" — also have infinite expectation, so wagering for God is not uniquely required.
5. Moral objection to belief-for-gain (Conclusion 2): even if rationality prescribes wagering, morality may prohibit it — Clifford's ethics of belief, and the charge that the divine plan is unjust.

Key evidence / textual basis

Clifford's rule is the moral core: evidentialism as "a rule of morality," on which "it is wrong always, everywhere, and for any one, to believe anything upon insufficient evidence" (SEP Pragmatic Arguments §3). His argument is itself pragmatic and social: believing on bad evidence makes one "credulous," and the danger "is not merely that it should believe wrong things... but that it should become credulous, and lose the habit of testing things and inquiring into them" (SEP Pragmatic Arguments §3). Applied to the Wager, this makes belief-for-reward a self-corruption. Pascal half-concedes the point: his own text admits the regimen "will... deaden your acuteness," and the SEP notes the original French, vous abêtira, means literally "will make you a beast" (SEP Pascal's Wager §5.5).

The many-gods objection is old and sharp. Diderot already saw that "an Imam could reason just as well this way," and J. L. Mackie presses that "the church within which alone salvation is to be found is not necessarily the Church of Rome, but perhaps that of the Anabaptists or the Mormons or the Muslim Sunnis or the worshippers of Kali or of Odin" (SEP Pascal's Wager §5.1). Cargile shows the deities are cheap: "for each real number x, consider the God who prefers contemplating x," so alternative gods are "a dime a dozen" (SEP Pascal's Wager §5.1). Mackie also targets the payoff, suggesting "a predestined infinite reward for the Chosen, whatever they do," which would flatten the decision table (SEP Pascal's Wager §5.1).

The infinite-utility and validity objections are the most technical. Some hold "the very notion of infinite utility is suspect," others that "an infinite reward could only be finitely appreciated by a human being," and strict finitists reject infinity outright (SEP Pascal's Wager §5.1). Worse for validity, Duff and Hájek show that mixed strategies tie the Wager: "toss a fair coin: heads, you wager for God; tails, you wager against," and by Pascal's own lights this has infinite expectation too — indeed "anything you might do is maximally good by expected utility lights," so there is no uniquely rational act (SEP Pascal's Wager §5.4). And the strict atheist escapes at premise 2: assigning p = 0, "Pascal's wager has no pull on strict atheists" (SEP Pascal's Wager §5.2). Penelhum adds the justice objection: the divine plan "is itself immoral, condemning as it does honest non-believers to loss of eternal happiness, when such unbelief is in no way culpable" (SEP Pascal's Wager §5.5).

Leading proponents

• W. K. Clifford — "The Ethics of Belief" (1877): the moralized evidentialist rule against belief on insufficient evidence; the credulity-and-society argument (corpus gap: essay via SEP Pragmatic Arguments §3, §7).
• J. L. Mackie — The Miracle of Theism (1982): concedes the Wager's validity while pressing the many-gods objection and the differing-decision-tables objection (corpus gap: via SEP Pascal's Wager §5.1, §5.4).
• Diderot, Cargile, Duff, Hájek, Penelhum, Voltaire — the many-gods, mixed-strategies, moral, and "indecency" strands, likewise via the SEP (SEP Pascal's Wager §5).

Strongest counter-arguments

Against Clifford, the standard reply is that his rule "is itself a moral pragmatic argument" and is arguably self-undermining, and that the "Duty Argument" produces cases — the "devious ETs," the doctor withholding a grim prognosis to preserve hope — in which pragmatic belief-formation is not merely permitted but morally required, so strong evidentialism (E) is false (SEP Pragmatic Arguments §7). Against many-gods, defenders argue that probabilities can serve as tie-breakers among infinite expectations, and that outlandish deities may be assigned lower probability for having "no backing of tradition" or lower simplicity (SEP Pascal's Wager §5.1). Against mixed strategies, Monton, and Easwaran and Monton, argue that a persistently re-run mixed strategy leads, "with probability 1," to wagering for God eventually (SEP Pascal's Wager §5.4).

Responses

The critics do not concede these repairs cheaply. The tie-breaker move imports a principle "not found in the Wager itself," and it is contested whether tradition or simplicity really privileges Pascal's God over rivals (SEP Pascal's Wager §5.1). Saka replies that Pascal's own peers "knew of Greco-Roman paganism, Judaism, Islam... and multiple brands of Protestantism," so restricting the live hypotheses to Catholicism and atheism is anachronistic (SEP Pascal's Wager §5.1). On the moral front, Clifford's heirs press that willful belief-cultivation "involves self-deception," "the deliberate worsening of one's epistemic situation" (SEP Pragmatic Arguments §8) — though the SEP notes this bites only against self-deceptive technologies, not against acceptance-plus-action, which need involve "no hint of self-deception" (SEP Pragmatic Arguments §8). The mixed-strategies rescue relies on idealizations (uncountably many die-rolls) that its authors admit are "surely not physically realizable" (SEP Pascal's Wager §5.4).

Assessment

Assessment: Live — the objections are collectively formidable: the mixed-strategies result genuinely threatens validity, the many-gods objection remains "the most important" premise-1 objection, and Clifford's moral challenge is not dissolved but redirected. None, however, is a knockdown: each has a live reply in the literature, and the strict-atheist escape (p = 0) simply exits the argument rather than refuting it (SEP Pascal's Wager §5.1, §5.4).

The Refined Defense

Abstract

The chastened form of the Wager retreats from the pretension to prove one should be Catholic and claims something narrower and steadier: that under genuine uncertainty atheism and agnosticism are irrational, that the Wager functions best as a tie-breaker within a tradition one already finds live, and as a spur to inquiry — a reason to keep seeking rather than a proof that terminates seeking. This is the James-flavoured "genuine option" framing married to Jeff Jordan's reconfigured wager. It concedes the many-gods objection's force, drops the claim to strong support, and rests on weak support: theistic commitment is one rational response among the live traditions, and refusing to engage the question is the one clearly unreasonable move.

Formal statement

Reconstructed from the SEP's treatment of Jordan's reconfiguration and James's weak-support reading (SEP Fideism §2.2.1; SEP Pragmatic Arguments §2):

1. Distinguish strong support (the argument shows theism alone yields the benefit) from weak support (theism is one of several ways) (SEP Pragmatic Arguments §2).
2. The many-gods objection defeats the Wager only as an argument for strong support; it leaves weak support untouched.
3. Among genuinely live options for a given agent, expected-utility considerations still favour wagering for God over the shared alternative of non-belief.
4. Therefore the Wager establishes not "Catholicism beats Islam" but "belief beats atheism and agnosticism," and rationally motivates continued inquiry into which live tradition is true.

Key evidence / textual basis

The refined reading is anchored in Pascal's own final movements, which are more modest than the headline calculus. The "fourth wager" argues that wagering for God dominates even setting probability aside, because one gains "in this life": "you will be faithful, honest, humble, grateful, generous, a sincere friend, truthful... you will thereby gain in this life... you have wagered for something certain and infinite, for which you have given nothing" (Pascal, Pensées fr. 233). The SEP reads this as a superduperdominance argument that holds "even if we allow that God's existence might be impossible" (SEP Pascal's Wager §6). And Pascal frames the Wager as a spur to inquiry, not a terminus: "But at least learn your inability to believe... Endeavour then to convince yourself, not by increase of proofs of God, but by the abatement of your passions" (Pascal, Pensées fr. 233). The following fragment makes the point explicitly: "According to the doctrine of chance, you ought to put yourself to the trouble of searching for the truth" (Pascal, Pensées fr. 236).

The contemporary refinement concedes many-gods and claims less. Jordan's "reconfigured wager" concedes the point and claims only "that atheism and agnosticism are irrational," not that one religion beats the others (SEP Fideism §2.2.1). James's argument is, by design, a weak-support argument: it "is intended to provide weak support" and claims only that religious belief is not less rational than unbelief, licensed where the option is genuine and open (SEP Pragmatic Arguments §2). This coheres with the SEP-life reading of Pascal himself: the calculation is "logically posterior to belief" and shows only that the believer's wager "is not unreasonable," a tie-breaker internal to a faith already found live rather than an external proof (SEP Pascal (life) §2). On this reading the Wager is best deployed exactly where William James deployed it — as the "clincher" that closes a genuine option the seeker already faces (SEP Pragmatic Arguments §3).

Leading proponents

• Blaise Pascal — read via the fourth ("superduperdominance") wager and the inquiry-fragments (fr. 233, 236): the Wager as spur to seeking and as internal tie-breaker, not external proof (SEP Pascal's Wager §6).
• William James — "The Will to Believe": the genuine-option framing and the explicit retreat to weak support (corpus gap: via SEP Pragmatic Arguments §2–3).
• Jeff Jordan (Pascal's Wager, 2006) and Schlesinger — the reconfigured wager and the probability tie-breaker; likewise via the SEP (SEP Fideism §2.2.1; SEP Pascal's Wager §5.1).

Strongest counter-arguments

Even the modest form is pressed. First, the self-deception residue: if one has no independent reason to prefer any tradition, cultivating belief in one may still be "the deliberate worsening of one's epistemic situation" (SEP Pragmatic Arguments §8). Second, the catching-belief dilemma for anyone (like Mill's hoper) who tries to act-as-if while withholding belief: the very practices that build commitment "tend to generate theistic belief," so the hope-only strategy is unstable (SEP Pragmatic Arguments §4). Third, the Pascal's Revenge twist: even assigning tiny probability p to Pascal's premises being right lets the mixed-strategies chaos back in, since p × ∞ = ∞ again (SEP Pascal's Wager §5.4). Fourth, whether "atheism and agnosticism are irrational" is genuinely established, or only relocated, by the retreat to weak support.

Responses

The defenders answer in kind. The self-deception worry is met by belief-inducing technologies that involve none — the acceptance-plus-action regimen, which "is a common way of generating belief" with "no hint of self-deception" (SEP Pragmatic Arguments §8). The catching-belief dilemma cuts for the Wager and against the hope-only halfway house: if acting-as-if reliably produces belief, then Pascal's regimen works as advertised, and only the person who wants the goods of faith without faith is trapped (SEP Pragmatic Arguments §4). To Pascal's Revenge, Jackson and Rogers argue the mixed-strategies objection is "structural, but not substantive," offering cases where "it is clearly rational to prefer one infinite good to another," and Hájek supplies "many valid reformulations of the Wager" on which lower probability of wagering yields lower expected utility (SEP Pascal's Wager §5.4). These reformulations do not restore the original's sweeping conclusion, but they preserve a defensible core.

Assessment

Assessment: Live — the refined Wager is the version most defenders now hold: a weak-support, tie-breaker, spur-to-inquiry argument that concedes many-gods, forgoes the claim to prove any particular creed, and rests on the more modest thesis that under genuine uncertainty active seeking beats settled non-belief. Its live burdens are whether "agnosticism is irrational" is earned rather than assumed, and whether the infinite-utility reformulations that answer Pascal's Revenge can be made rigorous without idealization (SEP Pascal's Wager §5.4).