Pragmatic and Prudential Arguments

Most arguments about God are epistemic: they aim to show that God exists, or that belief is warranted by evidence. The pragmatic (or prudential) arguments are different in kind: they grant that the evidence may be inconclusive and argue that it is nonetheless rational to believe — or to try to believe — on practical grounds, because of the benefits of believing or the costs of not. They concern the rationality of belief rather than the truth of the proposition, and they belong to the faith-and-reason and religious-epistemology debate over whether belief must be proportioned to evidence at all. The two landmarks are Pascal's Wager and William James's "The Will to Believe."

This page sets out the decision-theoretic structure of the Wager and its objections, James's reply to Clifford's evidentialism, and the problem of doxastic voluntarism that haunts both.

Pascal's Wager

Blaise Pascal (Pensées, §233) grants at the outset that theoretical reason cannot settle the question — "reason can decide nothing here" — and reframes belief as a decision under uncertainty, a bet one is forced to place by the very fact of living. The argument is a founding text of decision theory as much as of theology. With the two states (God exists / does not) and two acts (believe / not), the payoff matrix:

The reasoning runs through stages:

• Dominance fails to settle it alone, so Pascal computes expected utility. For any non-zero probability $p$ that God exists, the expected value of believing, $$\mathbb{E}[\text{believe}]=p\cdot (+\infty )+(1-p)\cdot (-f_1)=+\infty ,$$ infinitely exceeds the expected value of disbelief (finite). The infinite payoff swamps the finite stakes and any finite probability, however small. So the rational choice — by the agent's own prudential standard — is to wager for God.
• The voluntarist coda. Pascal anticipates the obvious reply — "I cannot make myself believe." His answer: belief is not directly willed but can be cultivated. Act as if you believed — "take the holy water, have masses said" — follow the practices, keep the company of believers, and belief will come "naturally," as the passions are tamed by habit. The will reaches belief indirectly, through action.

Objections

The Wager is ingenious but faces three serious objections:

• The many-gods objection. The matrix assumes a binary: the Christian God or no God. But there are indefinitely many possible deities, some of whom reward different beliefs, or punish the calculating Christian believer, or reward honest unbelief. Once the alternatives proliferate, the expected-value computation is scrambled — wagering for this God may incur the infinite penalty of another. Pascal's argument, run from a neutral starting point, does not single out which God to bet on.
• The doxastic-voluntarism objection. If belief cannot be chosen (see below), the Wager can at most recommend acting so as to induce belief — and a God who reads the self-interested, calculating motive behind such induced belief might be unimpressed, even offended. Belief adopted as a bet may not be the faith that is supposed to be rewarded.
• The mixed-strategy and infinite-utility objections. With infinite utilities the arithmetic misbehaves. If the reward is infinite, then any strategy that yields a non-zero probability of belief — believing fervently, believing half-heartedly, or even tossing a coin and believing if it lands heads — has infinite expected value too, since $ϵ\cdot \infty =\infty$ for any $ϵ>0$. So the Wager fails to recommend wholehearted belief over a token or probabilistic one (Duff, Hájek): every degree of belief "wins" equally, which trivialises the result. The mathematics of infinite expectations is genuinely pathological.

Defenders reply that the many-gods objection requires the rival deities to be equally probable and equally motivated, which the believer may deny on independent grounds, and that the infinite-utility problems can be eased by using large finite utilities (an afterlife of finite but enormous value), which preserves the practical recommendation without the pathologies — at the cost of the dominance the infinite version claimed.

James's "will to believe"

William James ("The Will to Believe," 1896) defends the right to believe on passional grounds, directly answering Clifford's rule that one must never believe on insufficient evidence. James's key notion is a genuine option — a choice between hypotheses that is:

• Living — both options are real candidates for the believer (not a dead, unappealing hypothesis);
• Forced — the options are exhaustive, with no third way: not choosing has the same practical upshot as choosing one side (to suspend belief in God is, practically, to live without God, just as denying it would);
• Momentous — the stake is unique, weighty, and (relatively) irreversible, not trivial or repeatable.

James's thesis: when an option is genuine and the evidence cannot decide it, we have the right to let "our passional nature" settle the matter — indeed we must, since suspension is itself a passional choice. He turns Clifford's rule against itself: "Do not believe anything upon insufficient evidence" is not a deliverance of evidence but a policy — the policy of one who fears error more than he loves truth. That is one legitimate temperament, but not the only rational one; a person who loves truth more than he fears error may rationally risk belief. And in forced, momentous cases, the rule of perpetual suspension can be self-defeating: it guarantees we miss a truth (and the good bound up with it) if the hypothesis is true, for some goods — friendship, love, certain cooperative ventures, and (James suggests) the religious relationship — become available only to those who first trust without proof. "Faith in a fact can help create the fact."

James is careful to limit the license: it applies only where the option is genuine and the evidence is genuinely undecidable. He does not license belief against the evidence, nor wishful thinking in ordinary, evidentially tractable matters (where Clifford is right). The religious hypothesis, James argues, is the paradigm of a genuine, forced, momentous, evidentially-open option — which is exactly why it is the case where the right to believe applies.

Doxastic voluntarism

Both arguments presuppose, and are threatened by, a thesis about the will and belief: doxastic voluntarism, the claim that belief is (at least partly) under voluntary control. The worry is that belief is not something we can decide to have — try to believe, right now, that there is a pink elephant in the room; you cannot simply will it. Belief seems responsive to evidence, not to choice; it happens to us in light of how things seem. If so:

• Pascal's Wager cannot recommend believing (an act not in our power), only acting so as to cultivate belief over time — which Pascal concedes and builds in, but which weakens "believe!" to "embark on a regimen that may produce belief."
• James's "will to believe" must likewise be read as indirect: the will permits and sustains a belief toward which one is already inclined in a genuinely open option, rather than manufacturing belief from nothing. James's actual target is the suppression of a belief one is drawn to, in deference to Clifford's rule — and that suppression is within voluntary reach.

Most philosophers accept at least indirect voluntarism: we cannot believe at will on the spot, but we can influence our beliefs over time by choosing what to attend to, investigate, and practise. Both pragmatic arguments are best understood as operating at this indirect level — recommending not an act of believing but a direction of the will and life that shapes belief.

Where the pragmatic arguments sit

The pragmatic arguments occupy a distinctive niche: they concede the epistemic question may be undecidable and argue that belief can still be rational to adopt on practical grounds — a move only available because they shift from truth to the rationality of believing. Pascal's Wager gives the prudential version (belief as the dominant bet under infinite stakes), powerful in structure but blunted by the many-gods, infinite-utility, and voluntarism objections; James gives the permissive version (the right, in genuine and evidentially-open options, to let the passional nature decide), a direct and influential answer to Clifford's evidentialism. Both must reckon with doxastic voluntarism, and both end up operating at the level of the will's indirect influence on belief rather than belief-on-command. They are not arguments that God exists but contributions to faith and reason: defenses of the rationality of religious commitment where proof is unavailable — close cousins of Reformed epistemology, which reaches a similar conclusion (belief can be rational without evidence) by an epistemic rather than a prudential route.