Miracles and Testimony

A miracle — an event that exceeds the productive power of nature and is attributed to God — has long played a double role in religion: as a direct argument for God's existence, and, more importantly, as the authentication of a revelation (the miracle stories of the founders, the Resurrection as the warrant of Christianity). The philosophical question is epistemic: under what conditions, if any, could the testimony that a miracle occurred make it rational to believe one did? The classic treatment is David Hume's "Of Miracles" (Enquiry, Section X), whose argument that testimony can never establish a miracle has framed every subsequent discussion — and which modern Bayesian reconstructions have both formalised and contested.

This page sets out the problem of defining a miracle, Hume's two-part argument and its critique of testimony, the Bayesian reconstruction (Earman's Hume's Abject Failure), and the Resurrection as the standard case study.

Defining a miracle

Before asking whether miracles are credible, one must say what they are, and the definition shapes the debate:

• Hume's definition: "a transgression of a law of nature by a particular volition of the Deity." A miracle is a violation of natural law — an event nature, left to itself, could not produce. This is the classical and most demanding conception, and it sets up Hume's argument: since a law of nature is, by definition, supported by uniform experience, a miracle is maximally improbable.
• The "violation" worry. Critics (Mackie notwithstanding, and many theists) find "violation" problematic. If an event occurs, in what sense is a law "violated" — should we not revise the supposed law? A law that has exceptions when God acts is not really a universal law. Alternatives: a miracle is a non-natural event — one brought about by an agent (God) not part of the natural order, not a violation of law but an input to the system "from outside" (much as my raising my arm is not a violation of physics but the action of an agent within it). Or, with Aquinas, a miracle is what is done by divine power outside the order usually observed in nature — graded into events nature could never do, events nature could do but not in this way/order, and events nature could do but God does without the natural means.
• The significance condition. Most accounts add that a genuine miracle is not a mere anomaly but a sign — religiously meaningful, expressive of divine purpose. A random unexplained event is not a miracle even if law-defying; the Resurrection or a healing means something.

The definitional choice matters: on the violation conception Hume's improbability argument bites hardest; on the non-natural-event conception a miracle need not be antecedently more improbable than any other rare agent-caused event.

Hume's argument

Hume's essay has two parts. Part I is the famous in-principle (a priori) argument; Part II is an empirical (a posteriori) argument that, in fact, no actual testimony has met the bar.

Part I — the balance of probabilities

Hume frames belief from testimony as a weighing of probabilities. The credibility of testimony rests on our experience that testimony is usually reliable; the credibility of a miracle is undercut by our experience that the laws of nature are uniform. So:

"A miracle is a violation of the laws of nature; and as a firm and unalterable experience has established these laws, the proof against a miracle, from the very nature of the fact, is as entire as any argument from experience can possibly be imagined."

The maxim that follows:

"No testimony is sufficient to establish a miracle, unless the testimony be of such a kind, that its falsehood would be more miraculous than the fact which it endeavours to establish."

That is: believe the miracle only if it would be even more improbable that all the witnesses are mistaken or lying than that the law-violating event occurred. Since the uniform experience supporting a law of nature is (Hume holds) the strongest possible empirical proof, while testimony is routinely fallible, the falsehood of the testimony is essentially never more miraculous than the miracle. So the rational person, "proportioning his belief to the evidence," should always reject the miracle report. This is meant as a standing result about the structure of the evidence, not about any particular case.

Part II — the empirical deficiencies

Hume then argues that, as a matter of fact, miracle testimony is also deficient on ordinary grounds: there has never been a miracle attested by sufficiently many witnesses of unquestioned good sense, education, and integrity; people have a natural appetite for wonder and the marvellous; miracle reports flourish chiefly among "ignorant and barbarous nations"; and the miracles of rival religions attest contrary systems and so cancel one another (a miracle supporting Christianity and one supporting Islam cannot both authenticate their incompatible doctrines, so each undermines the evidential force of the other).

Critiques of Hume

Hume's argument has been pressed hard from several directions:

• Circularity / question-begging. If "uniform experience" against miracles is what rules them out, Hume seems to assume that no miracle has ever occurred — for the experience is "uniform" only if every miracle report is already rejected. Whether a law is exceptionless is precisely what is in question; to treat the law as established by uniform experience is to presuppose the falsity of the reports one is assessing.
• It proves too much against rare events. Babbage and others noted that, by Hume's logic, we should reject testimony for any sufficiently unprecedented event — yet science and history routinely (and rightly) accept well-attested highly improbable occurrences (a particular lottery outcome, a novel scientific anomaly). Antecedent improbability is defeasible by strong enough testimony; Hume's maxim, read as a bar, is too strong.
• The weight of converging independent testimony. Hume underestimates how multiple independent witnesses can multiply credibility: even if each witness is individually unreliable, the probability that many independent witnesses all err in the same way can become vanishingly small — sometimes smaller than the prior improbability of the event. This is exactly the Bayesian point below.
• Definitional escape. On the non-natural-event (rather than violation) conception, a miracle is not maximally improbable given that a God exists who might act — so the prior is set by the existence-of-God question, not by "uniform experience" alone.

The Bayesian reconstruction

The modern treatment formalises the whole dispute with Bayes's theorem (confirmation theory). Let $M$ = "the miracle occurred" and $t$ = "the testimony that it occurred." The posterior probability is

$$P(M\mid t)=\frac{P(t\mid M)P(M)}{P(t\mid M)P(M)+P(t\mid \neg M)P(\neg M)}.$$

The miracle is credible on the testimony — $P(M\mid t)$ high — when the likelihood ratio

$$\frac{P(t\mid M)}{P(t\mid \neg M)}$$

is large enough to overcome the low prior $P(M)$. Hume's maxim is, in effect, the true observation that a low prior $P(M)$ requires a correspondingly tiny $P(t\mid \neg M)$ — the probability that the testimony would arise if the miracle had not occurred must be even smaller than the prior against the miracle. John Earman (Hume's Abject Failure, 2000) — himself no friend of miracles — argues that Hume's Part I is, as a general result, a failure: there is no a priori bar, because enough independent, reliable testimony can in principle drive $P(t\mid \neg M)$ low enough to make even a very improbable event credible. The question is quantitative and empirical, not settled by Hume's structural maxim. What survives is the Part II point, recast: whether, in any actual case, the testimony is good enough — numerous, independent, from reliable witnesses, without better naturalistic explanation — is a contingent matter to be assessed case by case. The interesting action is the prior: a convinced atheist sets $P(M)$ so low that almost no testimony suffices; a theist who antecedently grants a God who might act sets it high enough that good testimony can prevail. So the miracle debate is downstream of the existence-of-God debate.

The Resurrection as a case study

The Resurrection of Jesus is the standard test case (defended evidentially by Swinburne, the "minimal facts" argument of Habermas and Craig; contested by Ehrman and others). The dispute instantiates every element above:

• The prior $P(\text{Resurrection})$: near-zero for the naturalist; non-negligible for one who already finds theism probable and sees a fitting context (the life and claims of Jesus) in which God would act — illustrating that the case turns on background commitments.
• The likelihood ratio: defenders argue the "facts" (the empty tomb, the post-mortem appearances to many, the origin of the disciples' belief despite every disincentive) are very improbable unless the Resurrection occurred — i.e. $P(t\mid \neg M)$ is low. Critics offer naturalistic explanations (legend, hallucination, theft, misreport) that raise $P(t\mid \neg M)$ and so collapse the ratio.
• Hume's rival-religions cancellation: pressed by noting other traditions' miracle claims; answered by disputing their comparable attestation.

The case shows that "did the miracle happen?" is not resolved by a Humean a priori verdict but by the joint assessment of prior (set by the theism debate) and testimonial likelihood (set by history) — which is why believers and skeptics, assigning different priors, can rationally reach opposite verdicts on the same historical data.

Where miracles sit

Miracles are where the epistemology of testimony meets the existence of God, and Hume's "Of Miracles" remains the fixed point. His Part I maxim — that no testimony can establish a miracle unless its falsehood would be more miraculous — captures a genuine Bayesian truth (a low prior demands a correspondingly tiny chance of false testimony) but fails as an a priori bar: as Earman shows, sufficient independent testimony can in principle overcome any finite improbability, so the question is quantitative and case-by-case, not closed in advance. The decisive variable is the prior, and the prior is fixed by the arguments for and against God: to one who already judges theism improbable, miracle reports are nearly worthless; to one who grants a God who might act, good testimony can prevail — which is why the Resurrection debate is, at bottom, downstream of the existence debate rather than an independent proof. Like the argument from religious experience, miracle testimony is thus best seen not as a free-standing demonstration but as evidence whose weight depends on one's antecedent credence in theism — and, like all the routes to religious knowledge, as something the problem of evil and religious diversity press against from the other side.