Rowe's inductive and Draper's Bayesian arguments against theism, their Humean ancestry, and the skeptical-theist and theodicist replies
4Scholarly views
7Primary sources
5Scripture passages
3Related debates
Does the amount and distribution of apparently gratuitous evil make God's existence improbable?
Why it matters
The evidential argument from evil is where the argument from evil now lives. Its logical cousin — that God and evil are strictly incompatible — is widely regarded as answerable; the Stanford Encyclopedia's treatment, itself sympathetic to the argument, concludes that it "is surely best" to formulate it as "an evidential (inductive/probabilistic) argument for the more modest claim that there are evils that actually exist in the world that make it unlikely that God exists" (SEP §2). The live question is not whether God and a fawn's agony can coexist but whether, given the fawn's agony, God probably does not exist; an apologetic that answers only The Logical Problem of Evil has answered the easier half.
The debate has also become double-edged. Yujin Nagasawa's The Problem of Evil for Atheists (2024) argues that the problem arises for non-theists too — atheists who wield it violate the principle that "an argument against all is no argument against one" — and that "traditional theists can either win or draw while atheists/non-theists can at best draw but are more likely to lose" (Loke 2025, NDPR); Loke counters that this touches only naturalists, not supernaturalist atheists such as Buddhists.
A corpus note, as in The Kalam Cosmological Argument: the debate's primary papers — Rowe 1979, Draper 1989, Wykstra 1984, Bergmann 2001 — are copyright-locked. The views below are reconstructed from the two Stanford Encyclopedia treatments, which quote the originals extensively, and from the Dialogues Parts 10–11 of David Hume, the tradition's public-domain ancestor, given verbatim.
The argument
In its most-discussed direct form (following Rowe, as reconstructed in SEP §3.2):
There exist instances of intense suffering — a fawn dying in lingering agony in a forest fire (E1), a young girl brutally raped, beaten, and murdered (E2) — such that no good we know of would morally justify an omnipotent, omniscient being in permitting them.
Therefore, probably, no good at all would justify such a being in permitting them (the inductive step).
An omniscient, morally perfect being would prevent any evil it was not justified in permitting.
Therefore, probably, God does not exist.
Everything turns on step 2 — the inference from no good we know of to no good there is. The four views divide over that inference.
William L. Rowe gave the evidential argument its canonical modern form: from concrete cases of apparently pointless suffering, one projects inductively that some suffering really is pointless — which a perfectly good, all-powerful God would not permit. The deep root is Hume's Philo: the theist cannot infer divine goodness from a world like this, whatever consistency he salvages.
Formal statement
Rowe's inference, in his own notation (SEP §3.2.2):
(P) "No good state of affairs that we know of is such that an omnipotent, omniscient being's obtaining it would morally justify that being's permitting E1 or E2" (Rowe 1991, 72).
Therefore, probably, (Q) no good state of affairs at all would justify that being in permitting E1 or E2.
If God exists, some good would justify his permitting E1 and E2.
Therefore, probably, God does not exist.
A 1996 Bayesian variant derives Pr(G | P & k) < 0.5 from four probabilistic assumptions (SEP §3.4).
Key evidence / textual basis
P is not the mere report that we cannot see a justifying good but the stronger claim that every good we know of, on reflection, either could be obtained without permitting E1 or E2 or "wouldn't morally justify that being in permitting E1 or E2" (Rowe 1991, 72, at SEP §3.2.2). The fawn and the girl are chosen because their suffering "isn't the result of their own free will... nor does their suffering contribute to their 'soul-building'" (SEP-ST §1.2).
The Humean ancestry is direct. Philo revives "EPICURUS's old questions" — "Is he willing to prevent evil, but not able? then is he impotent. Is he able, but not willing? then is he malevolent. Is he both able and willing? whence then is evil?" — and, crucially for the evidential form, concedes compatibility while denying inferability: "A mere possible compatibility is not sufficient. You must prove these pure, unmixed, and uncontrollable attributes from the present mixed and confused phenomena, and from these alone" (Hume, Dialogues Part 10). Part 11 supplies the data: four circumstances "on which depend all, or the greatest part of the ills, that molest sensible creatures" — pain as motivator, government by general laws, the "great frugality" of creaturely powers, and nature's "inaccurate workmanship" — none of which "appear to human reason in the least degree necessary or unavoidable" (Hume, Dialogues Part 11). Scripture records the datum too: Hab 1:2-4 (bib); Ps 73:16-17 (bib).
Leading proponents
William L. Rowe — "The Problem of Evil and Some Varieties of Atheism" (1979); "Ruminations about Evil" (1991). Corpus gap: quoted via the SEP.
David Hume — Dialogues (1779), Parts 10–11, in corpus; the fountainhead.
Strongest counter-arguments
Three, in ascending force. First, Alvin Plantinga's: the P-to-Q inference is justified only if a justifying good, were there one, would likely be within our ken. Rowe replies that this demand "is simply to encourage radical skepticism concerning inductive reasoning in general" (1991, 73), and the SEP grants him that round against the criticism's crude form (SEP §3.2.2). Second, Michael Tooley's instantial-generalization objection: from "each unobserved A is probably B" it does not follow that "all unobserved As are probably B" — and Rowe needs the latter, since Q quantifies over all goods (SEP §3.2.3). Third, against the Bayesian variant: Rowe's P, interpreted so that ¬G entails it, is equivalent to "¬G or P*," and one's justification for it rests wholly on the second disjunct — violating the Total Evidence Requirement. The SEP's verdict: "Rowe's Bayesian argument is, therefore, unsound" (SEP §3.4.2).
Responses
Two lines survive. The inductive step can be rebuilt to concern particular actions rather than a universal generalization over goods — Tooley defends this via an equiprobability principle over unknown moral properties, yielding the theorem that given n events each apparently wrong to allow, the probability that none is objectively wrong to allow falls below 1/(n+1) (SEP §3.5). Alternatively, one may retreat to Draper's comparative strategy, which avoids the noseeum inference entirely. The cases' prima facie force is undisputed: even the providence literature concedes that "we are unable to discern any good coming from this single instance of evil, and the same could doubtless be said for millions of others" (SEP-Prov §1).
Assessment
Assessment: Live — the concrete cases still set the agenda and repaired versions survive, but the original inductive step and the Bayesian formulation are judged defective even by philosophers sympathetic to the conclusion (SEP §3.2.3, §3.4.2).
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Draper's Bayesian Argument
Stanceatheistic·Assessmentlive·ProponentsDraper Paul
Abstract
Paul Draper, explicitly "inspired by Hume," abandons the hunt for particular gratuitous evils. He compares theism with a rival hypothesis — the Hypothesis of Indifference — and argues that the observed distribution of pleasure and pain is much more probable on indifference; since indifference is no less plausible a priori and is incompatible with theism, theism is more likely false than true (SEP §3.3). Making no noseeum inference, it is standardly treated as the version most resistant to skeptical theism.
Formal statement
(HI) "Neither the nature nor the condition of sentient beings on earth is the result of benevolent or malevolent actions performed by nonhuman persons" (Draper 1989, 13).
Let O conjoin the facts about pleasure and pain: moral agents and sentient non-agents experiencing biologically useful pain and pleasure, and sentient beings experiencing pain and pleasure not known to be biologically useful.
Pr(O | HI) > Pr(O | T).
Pr(HI) ≥ Pr(T).
HI entails ¬T.
Therefore Pr(¬T | O) > Pr(T | O): "given the facts about pleasure and pain summarized by 'O', theism is more likely to be false than to be true" (SEP §3.3).
Key evidence / textual basis
The engine of premise 3 is biological: "given theism it is expectable that pleasure and pain would play additional roles beyond biological ones such as moral or religious roles (e.g., the virtuous receive pleasure, the vicious pain)" — yet we observe pain and pleasure calibrated to Darwinian fitness, as indifference predicts (SEP-ST §7.2).
The Humean template is Part 11's four-hypothesis passage: the first causes of the universe may have "perfect goodness," "perfect malice," both, or neither; "Mixed phenomena can never prove the two former unmixed principles; and the uniformity and steadiness of general laws seem to oppose the third. The fourth, therefore, seems by far the most probable" (Hume, Dialogues Part 11). Philo's ill-contrived-house analogy in the same Part carries the abductive point: "you would certainly blame the contrivance, without any further examination" (ibid.).
Leading proponents
Paul Draper — "Pain and Pleasure: An Evidential Problem for Theists" (Noûs 1989). Corpus gap: quoted via the two SEP entries.
David Hume — the comparative strategy is his; the SEP credits it as "originally used by David Hume in one of his arguments in his Dialogues" (SEP §3.1).
Strongest counter-arguments
The SEP catalogues five (SEP §3.3): (i) HI may not entail ¬T — God could have "created a neutral environment in which evolution could take place in a chancy way" and never intervened; (ii) Pr(HI) ≥ Pr(T) is contestable, HI being itself a sweeping universal generalization; (iii) the conclusion "says nothing at all about how much below 0.5" theism's probability falls; (iv) Peter van Inwagen attacks premise 3, though at the price of "quite an extraordinary claim" about establishing possibility; (v) most important, the total-evidence objection: other evidence O* — religious experience, or the design evidence Philo concedes strikes us "with such irresistible force" (Hume, Dialogues Part 10) — may favor theism, and it is far less clear that Pr(O & O* | HI) > Pr(O & O* | T). The skeptical-theist reply to Draper is given under the next view.
Responses
To (i) and (ii), Draper substitutes the Indifferent Deity Hypothesis — "There exists an omnipotent and omniscient person who created the Universe and who has no intrinsic concern about the pain or pleasure of other beings" (1989, 26) — which entails ¬T and matches theism's ontology, so "both of these objections can be avoided" (SEP §3.3). Against (iv), the SEP finds that such objections "tend to suggest that any flaws in Draper's argument in support of the crucial premise are less than obvious"; the inference-to-the-best-explanation form adds that the theistic explanation, unlike the indifferent-deity one, must postulate "additional, morally significant properties that lie beyond our ken," and is therefore less simple (ibid.). The total-evidence objection remains a cap, not a refutation: it concedes evil's evidential force and relocates the fight to the rest of the ledger — where The Fine-Tuning Argument and the resurrection evidence are entered on the other side.
Assessment
Assessment: Live — ranked by the skeptical-theism literature itself among "the most powerful arguments from evil" (SEP-ST §7.2); it resists CORNEA-style critiques by design, though the total-evidence objection limits what it can show.
Skeptical theism, reintroduced by Stephen J. Wykstra (1984) and given its most careful statement by Michael Bergmann (2001), attacks the evidential argument at its inductive joint: even if theism were true, we should not expect to discern all of God's reasons for permitting evil; so our failure to discern them is not good evidence that there are none (SEP-ST preamble). It is a defeater strategy, not a theodicy: the skeptical theist typically agrees that no known good justifies the fawn's suffering — and denies that this licenses any conclusion.
Formal statement
(Simple-CORNEA) "A person is prima facie reasonable in believing p on the basis of q only if, given their cognitive abilities, it is reasonable for them to believe that if p were different, then q would likely be different as well" (SEP-ST §1.3).
It is not reasonable to believe that if God's permission of E1 and E2 were necessary for some outweighing good, we would likely identify that good by reflection.
Therefore the "noseeum" inference from "we see no justifying good" to "there is none" fails.
Independently, Bergmann's theses: (ST1) "We have no good reason for thinking that the possible goods we know of are representative of the possible goods there are"; (ST2–ST3) likewise for possible evils and for the entailment relations between goods and permitted evils (2001, 279, at SEP-ST §2.2).
Therefore the sample-based inference from "no known good justifies" to "no good justifies" is also unreasonable.
Key evidence / textual basis
The supporting analogies are epistemic, not theological. A doctor who visually inspects a dropped needle is not reasonable in pronouncing it germ-free: his evidence would look the same either way (SEP-ST §1.3). Wykstra's parent/child analogy: "our cognitive abilities are like a baby infant's in comparison to God's" (cf. Wykstra 1984: 88, ibid.). The providence literature asks whether God's reasons are "most like, the elephants or the germs? Arguably... more like the germs" (SEP-Prov §10). Bergmann urges the theses on theist and non-theist alike: "it just doesn't seem unlikely that our understanding of the realm of value falls miserably short of capturing all that is true about that realm" (2001, 279).
The canonical scriptural warrant is the whirlwind speech of Job 38:1-7 (bib), where God answers the evidential complaint not with reasons but with a demonstration of the questioner's epistemic position; the mystery theme "is prominent in scriptural treatments of evil, such as those found in Job and Ecclesiastes" (SEP-Prov §10). Philo himself concedes the structure: one antecedently convinced the world is the work of "a very good, wise, and powerful Being... must allow, that there may be many solutions of those phenomena, which will for ever escape his comprehension" — his objection is that we are not antecedently convinced (Hume, Dialogues Part 11).
Leading proponents
Stephen J. Wykstra — the 1984 CORNEA paper that "reintroduced" the position "into the contemporary literature" (SEP-ST preamble).
Alvin Plantinga — pressed the original criticism of Rowe's P-to-Q inference; with William Alston, Peter van Inwagen, and Daniel Howard-Snyder among the principal developers (ibid.). Where evidentialists weigh evil on a public scale, Plantinga's Reformed epistemology adds that belief in God may be non-inferentially justified — the "Moore Switch" (SEP-Prov §10; SEP §6.2).
Strongest counter-arguments
Three families. Epistemological: CORNEA principles threaten regress and — McBrayer's objection — seem "inconsistent with forming reasonable beliefs on the basis of inductive evidence" (SEP-ST §5.1); worse, a theist who cannot rule out unknown divine reasons cannot rule out a "Deceiving God" either — threatening external-world skepticism (SEP-ST §5.3) — nor reasonably sift genuine from spurious divine commands, since that sifting "looks incredibly similar to the noseeum argument" (SEP-ST §5.4). Moral: skeptical theists apparently should never intervene against seemingly unjustified evils — "a kind of moral paralysis" — and seem committed to skepticism about all-things-considered value and obligation (SEP-ST §6). Scope: Draper's argument makes no noseeum inference, and non-inferential arguments and J. L. Schellenberg's hiddenness argument may also lie beyond reach (SEP-ST §7); Tooley adds that appeals to cognitive limitation provide "no reason at all" against the equiprobability version (SEP §5.1).
Responses
Wykstra and Perrine restrict CORNEA to "levering evidence" and recast its condition as a conditional probability, which "handles cases of inductive evidence" (SEP-ST §5.1); against external-world skepticism, Bergmann invokes epistemic externalism (SEP-ST §5.3). To moral paralysis: God may command intervention, and Wykstra's distinction between an evil being necessary for a good and its permission being necessary defuses the inference (SEP-ST §6.1); Howard-Snyder's dilemma argues any residual moral skepticism flows from one's moral theory, not from skeptical theism (SEP-ST §6.3). On scope: Perrine argues theism plus ST1–ST3 blocks the confident predictions Draper's comparative premise requires, and van Inwagen's hypothesis that the observed distribution of pain is "necessary for great goods... and for avoiding disvaluable worlds that are massively irregular" cannot be reasonably ruled improbable given theism (SEP-ST §7.2). The open worry is theory development: absorbing disconfirming data by adding skeptical theses risks making theism "a 'degenerating research program'" unless the additions are principled (SEP-ST §8).
Assessment
Assessment: Strong — the dominant theistic response, widely conceded to defeat the original noseeum formulations; its costs (potential religious and moral skepticism, limited scope against Draper and hiddenness) are the live frontier (SEP-ST §5–7).
Where the skeptical theist pleads ignorance of God's reasons, the theodicist names them. Richard Swinburne holds both that "theism does need a theodicy" and, optimistically, that "the required theodicy can be provided" (SEP §6.3, §7); the tradition's root is Augustine of Hippo's claim that omnipotent Goodness "would never permit the existence of anything evil among His works" unless able "to bring good even out of evil" (Augustine, Enchiridion ch. 11); its most influential modern form is John Hick's soul-making theodicy. Swinburne's program is probabilistic throughout — he coined "ramified" natural theology for Bayesian-style arguments extending to specifically Christian claims (SEP-NT §4) — so his theodicy is one component of a cumulative case, not a stand-alone proof.
Formal statement
God is justified in permitting an evil e if permitting e is necessary for an outweighing good (or avoiding a worse evil).
There are identifiable such goods — libertarian free will with genuine responsibility for others; virtue formed through struggle ("soul-making"); a law-governed world in which rational agency is possible — requiring the actuality or serious possibility of evils of the kinds we observe (SEP §7.1–7.4).
For a sufficiently impressive range of evils, it can be shown likely that an omnipotent, omniscient person would be justified in not preventing them; partial success licenses induction to the remainder (Swinburne 1988, 297–8, at SEP §6.3).
Therefore the evils of the world do not render theism improbable.
Key evidence / textual basis
Augustine supplies both the privation analysis — "what is that which we call evil but the absence of good?" (Augustine, Enchiridion ch. 11) — and the greater-good principle in its most audacious form: "God does well even in the permission of what is evil... the fact that evil as well as good exists, is a good. For if it were not a good that evil should exist, its existence would not be permitted by the omnipotent Good" (Augustine, Enchiridion ch. 96).
Hick's value-judgment anchors the soul-making version: "one who has attained to goodness by meeting and eventually mastering temptation... is good in a richer and more valuable sense than would be one created ab initio in a state either of innocence or of virtue" (1977, 255–6, at SEP §7.1). The providence literature develops this as the defeat (not mere outweighing) of evil: the argument falsely presumes the ideal creation is "a hedonistic paradise," yet "what we admire are lives of courage and sacrifice" (SEP-Prov §9). Swinburne's distinctive contribution is the freedom-to-do-great-evil thesis: free will's value scales with the moral range of the actions it governs, so a world where agents cannot seriously harm one another is a "'toy world', where one has very little responsibility for the well-being of others" (SEP §7.3); he also questions whether goods and evils are even "commensurable" on the common scale the argument presupposes (Swinburne 1998, ch. 13, at SEP-Prov §1). Scripturally the scheme rests on Rom 8:28 (bib) and 2 Cor 4:17 (bib). Corpus gap: Swinburne's The Existence of God (1979/2004) and Providence and the Problem of Evil (1998) are not in raw/; cited via the SEP entries.
Leading proponents
Richard Swinburne — "Does Theism Need a Theodicy?" (1988); Providence and the Problem of Evil (1998); the partial-success induction and toy-world argument.
Augustine of Hippo — Enchiridion (~420), chs. 11–12, 96; in corpus, quoted directly.
John Hick — Evil and the God of Love (1966/1977); soul-making.
Strongest counter-arguments
The SEP's survey is severe. Soul-making "provides no justification for the existence of any animal pain," none for the suffering of young children, and the world looks badly designed for the purpose (SEP §7.1). Free-will theodicies: the value of libertarian freedom "does not entail that one should never intervene in the exercise" of it — "almost everyone would hold that a failure to prevent heinously evil actions when one can do so would be seriously wrong" — and natural evils remain untouched (SEP §7.2). Against Swinburne's variant: great responsibility could be secured by the power to benefit enormously rather than to torture (SEP §7.3). Against natural-law theodicies: undetected interventions could have prevented the 1556 Shaanxi earthquake, the Black Death, or the Holocaust (SEP §7.4). J. L. Mackie's objection — God could have created beings with virtuous dispositions directly (1955, 205–6) — is pressed at SEP-Prov §9. From within theism, Plantinga calls most theodicies "tepid, shallow and ultimately frivolous" (1985a, 35, at SEP §7); and the partial-success induction, though reasonable in principle, is judged empty in practice since "no theodicy that has ever been proposed has been successful in the relevant way" (SEP §6.3).
Responses
The strongest replies invoke defeat rather than outweighing. To Mackie: "true virtue has to be tested and refined... It requires that we know trial and suffering... in the only way they truly can be known: through experience" (SEP-Prov §9). To apparently pointless suffering: compassion's object "is all suffering," so that "in this sense, at least, there is no such thing as suffering that serves no purpose"; and a world where every evil was "thoroughly and obviously defeated" would lack the very appearance of gratuitousness that calls forth the best in us (ibid.). Many theists, following van Inwagen, retreat from theodicy to defense — a story about God and evil "true for all anyone knows" — though the SEP presses hard on what probability such a story must itself have to blunt an evidential argument (SEP §4). Replies to animal and child suffering remain unresolved; theodicy carries the heaviest burden of the four views, which is why most defenders combine it with skeptical theism for the residue (SEP-ST §4).
Assessment
Assessment: Live — the soul-making and free-will strands have real force against abstract formulations, but no proposed theodicy is generally judged to cover animal pain, child suffering, and the quantity of natural evil; the position survives chiefly in combination with skeptical theism (SEP §7).
The evidential argument deserves to be felt before it is answered; Scripture gives Job, Habakkuk, and Asaph its data in the first person. The debate's present state shows this much: no one has demonstrated that the fawn's suffering is gratuitous — the inference from "we see no reason" to "there is no reason" is shakier than it first appears — and no one has produced a theodicy that names God's reasons to general satisfaction either. The believer is left roughly where Job was left: with a God who declines to submit his reasons for audit, and with the question of whether the rest of what we know — creation, conscience, Christ — is weighty enough to trust him in the dark. The skeptic should notice that the strongest surviving form of the argument yields at most "more likely false than true, on this evidence alone," and that the newest scholarship asks whether the atheist can account for the goodness against which evil is measured. Neither side should claim the verdict is in.
Last compiled: 2026-07-04 by pass-poe-evidential-001
Last compiled: 2026-07-04 · 7 primary sources · 4 views · archetype A