Miracles

The philosophical analysis of miracles concerns three fundamental questions: what constitutes a miracle, whether miracle claims can ever be rationally believed, and what criteria should govern the evaluation of miracle testimony. These questions intersect with epistemology, philosophy of religion, philosophy of science, and probability theory. Since David Hume’s celebrated discussion in Section X of his Enquiry Concerning Human Understanding (1748), the miracle question has been one of the most persistently debated topics in Western philosophy, generating a literature that spans metaphysics, the nature of natural law, Bayesian probability, and the epistemology of testimony.^{1, 4}

The stakes of the debate are high. Miracle claims feature centrally in most theistic traditions as evidence of divine action in the world. If such claims can be rationally justified, they constitute a powerful form of evidence for natural theology; if they cannot, a significant category of religious evidence is undermined. The philosophical discussion is therefore not merely academic but bears directly on the rationality of religious belief and the argument from miracles for God’s existence.^{4, 5}

Definitions of miracle

The way one defines “miracle” substantially determines what follows in the philosophical analysis. Three definitions have been especially influential, and they differ in ways that carry significant consequences for the question of whether miracles are possible and detectable.

The most widely discussed definition comes from David Hume, who characterized a miracle as “a transgression of a law of nature by a particular volition of the Deity, or by the interposition of some invisible agent.” On this account, a miracle is defined by two features: it violates an established law of nature, and it is caused by a supernatural agent. Hume’s definition has the virtue of clarity but has been criticized for building in assumptions that may prejudge the philosophical question. If natural laws are defined as exceptionless regularities, then by definition nothing can violate them — any apparent violation simply shows that the supposed law was not a genuine law after all. This circularity concern has motivated alternative definitions.^{1, 4}

Richard Swinburne proposed an influential alternative in The Concept of Miracle (1970). He defined a miracle as a “non-repeatable counter-instance to a law of nature,” carefully distinguishing this from a violation. On Swinburne’s account, a law of nature is a generalization about what happens under certain conditions when no external agent intervenes. A miracle occurs when the outcome differs from what the law predicts, not because the law is wrong, but because a non-natural cause has acted. The law remains valid as a description of what nature does on its own; the miracle is simply a case where nature was not left on its own. This preserves the integrity of scientific laws while allowing for the logical possibility of divine intervention.^{2, 4}

Robert Larmer offered a third approach, defining a miracle as a divine intervention that alters the natural order by introducing new causal factors. Larmer argued that miracles do not violate natural laws any more than a person catching a falling ball violates the law of gravity. The law of gravity continues to operate; additional forces are simply introduced. On this “interventionist” model, God acts within the natural order by adding causal inputs that change outcomes while leaving the underlying laws intact. This definition avoids the conceptual difficulties of the violation model while preserving the theological claim that miracles involve genuine divine action in the physical world.^{7, 14}

A quite different approach was proposed by R. F. Holland in 1965. Holland argued that a miracle need not involve any violation of natural law at all. On his account, a “contingency miracle” occurs when a coincidence of natural events is religiously significant — when, for instance, a child is saved from an oncoming train by a mechanical failure that stops the engine at precisely the right moment. No law of nature is broken, but the event may be experienced as miraculous within a framework of religious interpretation. Holland’s definition shifts the concept of miracle from the metaphysical to the hermeneutical, making it a function of how events are interpreted rather than what kind of causal process produced them.^{13, 4}

The medieval tradition, especially as articulated by Thomas Aquinas, defined miracles in terms of divine power exceeding the capacity of any created nature. Aquinas distinguished three grades of miracle: events that nature can never produce (such as two bodies occupying the same space), events that nature can produce but not in the relevant subject (such as restoring sight to the blind), and events that nature can produce but not in the manner that occurs (such as an instantaneous cure of fever). This graded taxonomy reflects a premodern understanding of natural law as the regular operation of created natures under divine governance, where miracles represent God acting beyond those natures without contradicting them.^{19, 4}

Hume’s in-principle argument

Hume’s discussion of miracles in Section X of the Enquiry (1748) is typically divided into two parts, often called the “in-principle” argument and the “in-fact” argument. The in-principle argument, presented in Part I of Section X, offers a general epistemological framework for evaluating miracle testimony. Hume begins from the premise that a wise person proportions belief to evidence. The evidence for a law of nature, he argues, consists of a uniform experience — the repeated, exceptionless observation that nature behaves in certain ways. The evidence for a miracle, by contrast, consists of testimony that on a particular occasion nature behaved differently. The rational assessment of a miracle report therefore requires weighing the strength of testimony against the strength of the evidence for the law that the miracle allegedly violated.^{1, 11}

Hume’s central contention is that this weighing will always favour the law of nature. The evidence for a natural law is, by hypothesis, uniform and extensive — it represents the totality of human experience with respect to the regularity in question. Testimony, however strong, can never fully counterbalance this weight. Even the most reliable witnesses can be mistaken, deceived, or deceiving; the possibility of error in testimony is always non-zero. Therefore, Hume concludes, “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.” This famous maxim does not strictly assert that miracles are impossible, but it sets the evidential bar so high that, in practice, testimony alone can never meet it.¹

P1. A wise person proportions belief to the evidence.

P2. The evidence for a law of nature consists of uniform, extensive experience.

P3. The evidence for a miracle consists of testimony that this uniform experience was violated on a particular occasion.

P4. Testimony is never so strong that its falsehood would be more improbable than the event it reports.

C. Therefore, testimony is never sufficient to establish a miracle.

Interpreters disagree about the precise logical structure of Hume’s argument. Some, following Antony Flew, read Hume as presenting an argument about the balance of evidence: since the evidence for a law of nature is maximal, no testimony can outweigh it. Others read the argument more modestly, as claiming only that the prior improbability of a miracle is always very high, so that correspondingly extraordinary evidence is required to overcome it. The second reading is more defensible and more naturally accommodates a Bayesian reformulation, though it may not capture Hume’s own intention, which appears more categorical.^{12, 3}

Hume’s in-fact argument

In Part II of Section X, Hume supplements the in-principle argument with four empirical observations about the actual state of miracle testimony, which collectively constitute the “in-fact” argument. These are not deductive conclusions but inductive generalizations about the character of miracle reports as they have historically been made.^{1, 4}

First, Hume observes that no miracle has ever been attested by a sufficient number of witnesses of good sense, education, learning, and reputation — witnesses whose social standing and character would make it especially costly and implausible for them to be mistaken or dishonest. Second, he notes the natural human tendency toward the marvellous: people take pleasure in wonder and surprise, and this psychological disposition creates a systematic bias toward accepting and embellishing extraordinary reports. Religious enthusiasm, Hume argues, amplifies this tendency. Third, miracle reports are most abundant among “ignorant and barbarous nations,” and when they appear in civilized societies, they invariably originate from an earlier period when the population was less educated. Fourth, the miracle claims of different religions cancel each other out: the miracles attested in Christianity, Islam, Hinduism, and other traditions are mutually inconsistent, since each tradition uses its miracles to establish a theological framework that contradicts the others. Any miracle offered in support of one religion is therefore simultaneously evidence against every other religion and its miracles.^{1, 11}

The in-fact arguments have been evaluated differently from the in-principle argument. Many philosophers regard them as sociological observations that have some force but are not philosophically decisive. The claim that no miracle has ever had sufficiently credible witnesses is an empirical assertion that proponents of miracles contest directly, pointing to cases they regard as well-attested. The mutual cancellation argument has been more influential, though critics note that it assumes miracle claims from different traditions must be in direct competition — an assumption that a theist who believes in one God active across multiple cultural contexts might reject.^{5, 17}

Responses to Hume

Hume’s argument has attracted criticism from multiple directions, and the responses have sharpened considerably with the tools of modern probability theory. The earliest significant response came from Hume’s own century. Charles Babbage, in The Ninth Bridgewater Treatise (1838), argued that Hume had committed a mathematical error. Using the calculus of probabilities as developed by Laplace, Babbage showed that if testimony is sufficiently reliable, there exists a calculable point at which the probability that the testimony is true exceeds the probability that it is false, even for extremely improbable events. The key insight was that Hume had treated the improbability of the miracle as fixed and maximal while ignoring the compounding evidential force of independent, reliable witnesses.^{15, 3}

The most sustained modern critique is John Earman’s Hume’s Abject Failure (2000). Earman, himself an atheist with no interest in defending miracle claims, argued that Hume’s argument is logically flawed on its own terms. Earman’s central objection is that Hume conflates the prior probability of a miracle with the posterior probability after testimony is received. In Bayesian terms, even if the prior probability of a miracle is extremely low, sufficiently strong testimony can raise the posterior probability to a level that warrants belief. Hume’s argument works only if no testimony can ever be strong enough to overcome the prior improbability — but this is precisely what needs to be shown, not assumed. Earman concludes that Hume’s argument, as stated, either begs the question or is demonstrably invalid when properly formalized.³

Richard Swinburne has responded to Hume on different grounds. In The Existence of God (2004), Swinburne argues that Hume neglects the relevance of background knowledge. If there are independent reasons to think that God exists — from cosmological, teleological, or other arguments — then the prior probability of a miracle is not as low as Hume assumes. The probability that God would intervene in a particular way depends on what we know about God’s nature and purposes. On Swinburne’s view, the assessment of miracles cannot be separated from the broader question of theism: a person who has good reason to believe in God should assign a higher prior probability to miracles and therefore requires less testimony to be rationally convinced.^{5, 8}

Timothy and Lydia McGrew have offered a detailed Bayesian analysis of specific miracle claims, particularly the resurrection of Jesus. In their contribution to the Blackwell Companion to Natural Theology (2009), they argue that when the evidence for the resurrection is evaluated using Bayes’s theorem — considering the reliability of the sources, the number of independent witnesses, and the alternative explanations available — the posterior probability of the resurrection is very high, even on modest assumptions about the prior probability. Their analysis attempts to show that Hume’s dismissal of miracle testimony fails not merely in principle but when applied to specific, well-documented cases.⁹

Not all responses to Hume have been critical. Robert Fogelin’s A Defense of Hume on Miracles (2003) argues that Hume’s critics have misread the argument. Fogelin contends that Hume is not offering a prior probability argument that can be overturned by sufficient testimony, but rather making the more radical claim that the very concept of a law of nature entails that the evidence against a miracle is always maximal. On Fogelin’s reading, Hume’s argument is not about the mathematics of probability at all, but about the epistemological status of natural laws as the strongest possible form of evidence. This interpretation makes the argument more resistant to Bayesian critique but also more controversial, since it seems to rule out miracles by definitional fiat.¹⁰

Bayesian approaches to miracle testimony

The application of Bayes’s theorem to miracle testimony has become the dominant framework for contemporary discussion. In its simplest form, the theorem states that the posterior probability of a miracle (M) given testimony (T) is proportional to the prior probability of the miracle multiplied by the likelihood of receiving such testimony if the miracle occurred, divided by the overall probability of receiving such testimony:

P(M|T) = [P(M) × P(T|M)] / P(T)

This framework clarifies several aspects of the debate. First, it shows that the posterior probability of a miracle depends on three factors: the prior probability of the miracle, the probability that the testimony would arise if the miracle actually occurred, and the probability that the testimony would arise from all causes combined (including fraud, hallucination, legendary development, and honest error). A miracle with an extremely low prior probability can still receive a high posterior probability if the testimony is of a kind that would be very unlikely to arise in the absence of the actual miracle.^{3, 18}

Second, the Bayesian framework reveals the central importance of the “false positive rate” — the probability of receiving miracle testimony when no miracle has occurred. If this rate is high (because people are prone to religious enthusiasm, cognitive biases, or cultural expectations of the miraculous), then even reliable testimony adds less evidential force than it might initially appear to carry. Conversely, if the false positive rate is very low (because the witnesses had no motive to fabricate, the cultural context did not encourage miracle claims, and the testimony was costly to maintain), the evidential force of the testimony is correspondingly greater.^{18, 9}

Peter Millican has argued that the Bayesian framework, properly applied, actually supports a version of Hume’s conclusion. Millican contends that when one considers the base rate of miracle claims across all of human history — the vast number of reported miracles that turned out to have natural explanations or were later discredited — the false positive rate for miracle testimony is extremely high. This means that even testimony that appears individually strong is overwhelmed by the background frequency of false miracle reports. The problem is analogous to medical screening: a test with 99% accuracy will still produce mostly false positives if the condition being tested for is extremely rare.¹⁸

Bayesian components in miracle testimony evaluation^{3, 18}

The base rate problem

One of the most significant difficulties in the Bayesian analysis of miracles is the base rate problem: how does one determine the prior probability that a miracle has occurred? This question has no straightforward empirical answer, and the value assigned to the prior probability largely determines the outcome of the calculation.^{3, 4}

Sceptics argue that the base rate for genuine miracles is effectively zero or vanishingly small. The reasoning is inductive: throughout the history of science, purported miracles and supernatural interventions have consistently been explained by natural causes as scientific knowledge has expanded. Every investigated case of spontaneous combustion, faith healing, weeping statues, and similar phenomena has yielded natural explanations when subjected to rigorous scrutiny. This track record, sceptics contend, provides strong grounds for assigning an extremely low prior probability to any new miracle claim.^{17, 4}

Theists respond that the base rate question cannot be answered without reference to background beliefs. If God exists and has the character traditionally ascribed to God in monotheistic theology — a being who is personal, benevolent, and interested in human affairs — then the prior probability that God would occasionally act in the world in extraordinary ways is not negligible. On this view, the base rate for miracles is not determined by the frequency of past confirmed miracles but by the probability of theism itself. Swinburne has argued that if the probability of theism is even moderately high (say, 0.5 based on independent arguments from cosmology, fine-tuning, and morality), then the prior probability of specific miracles in specific contexts may be substantial.^{5, 8}

The base rate problem thus reveals a deep structural feature of the miracle debate: the assessment of miracle claims is not independent of one’s prior metaphysical commitments. A naturalist who assigns a prior probability of zero (or near zero) to theism will find virtually no testimony sufficient to establish a miracle. A theist who assigns a moderate prior probability to God’s existence will find some miracle testimony compelling. This is not a defect of the Bayesian framework but a reflection of the fact that miracle claims are embedded within larger worldview disputes that cannot be resolved by testimony alone.^{3, 5}

The role of background beliefs

The dependence of miracle assessment on background beliefs has been a central theme in recent philosophical discussion. The issue goes beyond the prior probability of theism to encompass a range of background assumptions about how the world works, what kinds of evidence are relevant, and what counts as a satisfactory explanation.^{4, 5}

John Locke, writing before Hume, articulated an early version of this insight. In the Essay Concerning Human Understanding (1690), Locke argued that the credibility of any testimony depends in part on its “conformity to our own knowledge, observation, and experience.” A report that conforms to what we already know about the world is easier to credit than one that contradicts our experience. But Locke also recognized that this principle, taken to an extreme, would make it impossible ever to learn anything genuinely new through testimony. If conformity to prior experience were the sole criterion for accepting testimony, no one could ever rationally believe a traveller’s report of previously unknown phenomena. Locke therefore allowed that testimony from reliable witnesses could justify belief in events that transcend the hearer’s experience, provided the witnesses were credible and numerous.²⁰

Hume himself, in the posthumous Dialogues Concerning Natural Religion (1779), explored the broader question of how background beliefs shape the evaluation of evidence for theological claims. The character Philo argues that the further a hypothesis extends beyond ordinary experience, the less confidence we can have in analogical reasoning about it — a principle that bears directly on miracle claims, since they ask us to reason about divine action on the basis of human experience with natural causes.¹⁶

J. L. Mackie, in The Miracle of Theism (1982), took up the question of background beliefs from a sceptical perspective. Mackie argued that the evidence for a miracle must be assessed not merely against the specific law of nature allegedly violated, but against the entire body of evidence for the regularity of nature. This total evidence includes not just the particular law in question but the general success of science in explaining phenomena without recourse to supernatural intervention. Mackie concluded that the background evidence for naturalism is so strong that miracle claims face an almost insuperable evidential burden. His argument is more modest than a blanket rejection of miracles: he allows that they are logically possible but argues that, given our total background evidence, they are never the best explanation of the available data.¹⁷

Swinburne has responded that Mackie’s appeal to the general regularity of nature is too broad. The fact that nature generally operates in lawful ways does not by itself make it improbable that God would occasionally intervene. To think otherwise would be like arguing that because a king generally follows routine procedures, it is improbable that the king would ever issue a special decree. The regularity of nature, Swinburne contends, is fully compatible with occasional divine intervention, and the evidence for natural law does not count against miracles unless one has already assumed that God does not act in the world.⁵

Spinoza’s critique

Baruch Spinoza’s critique of miracles, articulated in the Tractatus Theologico-Politicus (1670), precedes Hume’s by nearly a century and differs from it in important respects. Where Hume argued that miracles are epistemically unjustifiable — that we can never have sufficient reason to believe one has occurred — Spinoza argued that miracles are metaphysically impossible. On Spinoza’s pantheistic metaphysics, God and nature are identical: Deus sive Natura. The laws of nature are the decrees of God, and they follow necessarily from God’s nature. For God to violate a law of nature would be for God to contradict God’s own nature, which is impossible. Miracles, understood as violations of natural law, are therefore not merely undetectable or unlikely; they are conceptually incoherent.^{6, 4}

Spinoza also advanced an epistemological argument. He contended that if miracles occurred, they would actually undermine rather than support belief in God. Knowledge of God, Spinoza reasoned, comes through knowledge of the fixed and immutable order of nature. If that order were disrupted by arbitrary interventions, our knowledge of God would be undermined rather than confirmed. A God who needs to interrupt the natural order is, on Spinoza’s view, a God whose original creation was deficient — a conclusion that Spinoza regarded as incompatible with genuine divinity. This argument has been influential among those who hold that miracles are theologically as well as philosophically problematic.⁶

Spinoza’s critique depends on his particular metaphysical system, and most participants in the contemporary debate do not share his pantheism. Classical theists who distinguish God from nature reject the premise that God’s decrees are identical with the laws of nature, and therefore find no incoherence in the idea of divine intervention. Nevertheless, Spinoza’s argument has been historically significant as the first systematic philosophical attempt to rule out miracles on conceptual grounds, and it anticipates the deterministic objections to miracles that recur in later Enlightenment thought.^{4, 6}

Miracles and the philosophy of natural law

Much of the philosophical debate about miracles turns on what one takes a law of nature to be. Different accounts of natural law yield different assessments of whether miracles are possible, and if so, what it would mean for one to occur.^{4, 2}

On a regularity account of natural laws — the view that laws are simply descriptions of exceptionless regularities in nature — miracles face a conceptual problem. If a law just is a description of what always happens, then an exception to the law shows that the supposed law was never a true law. The “miracle” is not a violation of a law but a falsification of a proposed regularity, which must now be revised to accommodate the exception. On this account, miracles in Hume’s sense are impossible by definition: if an event occurs, it is part of the regularities of nature, and no law has been violated. This is one source of the circularity objection to Hume’s argument.^{17, 4}

On a necessitarian or essentialist account — the view that laws reflect necessary connections between properties or the essential dispositions of natural kinds — miracles appear to require the overriding of causal powers that things possess essentially. Whether this is possible depends on whether God has the power to override the causal dispositions of matter. Most theists who hold this view answer affirmatively, arguing that God, as the creator of matter and its dispositions, can act on matter in ways that transcend its natural capacities.^{14, 7}

On a best-systems account, associated with David Lewis and others, laws are the axioms of the deductive system that best balances simplicity and strength in describing the actual history of the world. On this view, an isolated miracle — a single exception in the entire history of the universe — might not affect which generalizations count as laws, because the best system might still include the generalization with the understanding that it holds in all but one instance. This account potentially makes space for miracles without undermining the concept of natural law, though it also raises the question of whether a “law” with known exceptions is really a law at all.⁴

Larmer has argued that the entire debate over miracles and natural laws rests on a false dichotomy. Laws of nature, he contends, describe what happens in a causally closed system. A miracle does not violate a law because it involves the introduction of a new causal factor — divine action — that the law was never intended to account for. Just as the trajectory of a billiard ball is not “violated” when another ball strikes it, the laws of nature are not violated when God introduces new causal inputs. On this view, the miracle is fully natural in the sense that the laws of nature continue to operate; what is supernatural is only the source of the additional causal input.^{7, 14}

Current state of the discussion

The philosophical debate over miracles remains active and unresolved, but several points of convergence have emerged. First, there is broad agreement that Hume’s argument, in its strongest form, is not a simple deductive proof that miracles cannot occur or cannot be believed. The argument is better understood as a claim about evidential probabilities, and as such it can be engaged with the tools of Bayesian probability theory. Whether the argument succeeds depends on empirical and metaphysical assumptions that Hume does not establish within the argument itself.^{3, 10}

Second, the Bayesian framework has made it clear that the miracle question cannot be separated from the question of theism more broadly. The prior probability of a miracle is not a freestanding quantity but is conditioned on one’s assessment of whether God exists and, if so, what kind of God exists. This means that the miracle debate is, at bottom, a proxy for the theism-naturalism debate: those who have independent reasons for theism will find miracle claims more plausible, and those who do not will find them less so. The testimony itself is rarely the decisive factor.^{5, 18}

Third, the definitional question remains consequential. Whether one defines miracles as violations of natural law, non-repeatable counter-instances, divine interventions, or religiously significant coincidences affects every subsequent step of the analysis. No single definition has achieved consensus, and the choice of definition often reflects prior metaphysical commitments rather than following from neutral philosophical analysis.^{4, 2}

Fourth, the epistemology of testimony has become a field of its own, and developments in that field bear on the miracle question. Work on the reliability of eyewitness testimony in psychology and forensic science, on the mechanisms of memory distortion and confabulation, and on the social dynamics of rumour transmission has generally reinforced the sceptical side of the debate by documenting the many ways in which testimony can be unreliable, especially for unusual or emotionally charged events. At the same time, epistemologists of testimony such as C. A. J. Coady have argued that a general scepticism about testimony is self-undermining, since our knowledge of the very regularities that Hume invokes depends on testimony from other observers.^{4, 18}

Finally, the debate has increasingly recognized the distinction between the general philosophical question — can miracle claims ever be rationally justified? — and the particular historical question — did this miracle actually occur? Philosophers such as the McGrews have argued that the general question is less interesting than the particular one: the real issue is whether specific miracle claims, evaluated on their own terms with the available evidence, meet the relevant evidential threshold. This shift from the general to the particular has made the debate more empirically grounded but also more dependent on detailed historical scholarship, moving the conversation beyond what philosophical analysis alone can settle.^{9, 5}

The philosophy of miracles thus remains a live area of inquiry precisely because it sits at the intersection of epistemology, metaphysics, philosophy of science, and philosophy of religion. The question of whether miracles can be rationally believed is, in the end, inseparable from the question of what kind of universe we inhabit — and that question, as the ongoing debate attests, admits of no easy or universally accepted answer.⁴