In discussions about the existence of God, miracles, or other claims deemed supernatural, the maxim "extraordinary claims require extraordinary evidence" is frequently invoked. Carl Sagan popularized the slogan, but the underlying thought is older: Laplace is commonly associated with the idea that the weight of evidence should be proportioned to the strangeness of the reported fact, and David Hume's discussion of miracles similarly weighs testimony against background probability. The serious version is therefore not merely "strange claims should be mocked"; it is a proposed rule of rational proportion between a claim's prior probability and the strength of the evidence for it. The question is whether that rule is coherent, and whether it is sometimes used in debates about God in a way that assumes atheistic background commitments rather than arguing for them.
What Makes a Claim 'Extraordinary'?
At the heart of Sagan's maxim is the notion of an "extraordinary" claim. In its strongest form, a claim is extraordinary not simply because it is unfamiliar, religious, or unpopular, but because it has a low prior probability relative to our total background knowledge. That may happen when the claim conflicts with well-confirmed theories, when it would force revisions to many other justified beliefs, or when there are many more ordinary explanations available. For example, a report of unaided human levitation would normally be extraordinary because, given what we know about bodies, gravity, illusion, and testimony, the claim starts with a very low prior probability.
However, this raises a significant question: who sets the baseline for what is considered "ordinary"? The baseline cannot simply be one person's worldview or the assumptions of a particular community. It should be the best publicly available background evidence: established science, reliable experience, historical knowledge, and broader philosophical considerations. Nor should "extraordinary" mean "not yet explained by current science." Open questions are not automatically evidence against a claim, and genuine scientific revolutions are possible. The better point is narrower: when a claim is in serious tension with a large body of well-supported background knowledge, a rational person will need correspondingly strong evidence before accepting it.
Is the Principle Itself Extraordinary?
A common reply is to ask whether the principle "extraordinary claims require extraordinary evidence" is itself an extraordinary claim. This is a useful pressure test, but it should be aimed at the strongest version of the maxim. The principle is not normally meant to say that every belief requires spectacular proof. In ordinary life, we rightly accept many claims on modest testimony because they fit well with background knowledge: that a friend visited a shop, that a train was delayed, or that a battle occurred in a well-attested historical period. The real issue is whether a much less expected claim should require evidence that is not merely sincere or interesting, but strong enough to overcome its initial improbability.
So the principle is not best treated as an "extraordinary" empirical claim about the world, like a claim about levitation. It is a proposed norm of reasoning. Norms of reasoning do require justification, but not the same kind of evidence as reports of rare events. The self-referential objection works only against a crude version of the slogan: "anything surprising may be dismissed unless it comes with impossible proof." Against the more careful Bayesian version, the better question is not whether the maxim refutes itself, but whether its key terms - "extraordinary," "evidence," and "require" - can be made precise without smuggling in controversial assumptions.
Bayesian Reconstruction: A Strong Defence
One of the strongest defences of Sagan's maxim comes from Bayesian confirmation theory, a standard framework in contemporary epistemology and philosophy of science. In Bayesian terms, evidence does not float free from background knowledge: it updates a prior probability into a posterior probability. Roughly, posterior odds equal prior odds multiplied by the evidential force of the data, often called the likelihood ratio or Bayes factor. A claim with a very low prior probability can therefore become credible, but only if the evidence is much more likely on that claim being true than on its rivals. John Earman, for example, treats Hume's argument about miracles as best assessed in probabilistic terms, even while criticizing Hume's own case against miracles.
From a Bayesian perspective, then, the maxim is not an arbitrary demand but a reflection of proportional updating. If a claim is initially unlikely, the evidence required to make it credible must be correspondingly strong. "Strong" here need not mean exotic or theatrical; it means evidence that is much more expected if the claim is true than if it is false. Multiple independent lines of evidence, reliable public observation, successful prediction, or the failure of plausible alternative explanations can all raise the probability of a claim. This also means that the maxim by itself does not decide theism, atheism, or miracles. The prior probabilities and the evidential comparisons still have to be argued.
The Bayesian approach clarifies that the principle is not about dismissing extraordinary claims outright but about calibrating the strength of evidence needed to justify belief in them. In that limited form, the principle is reasonable and methodologically defensible. But this defence also disciplines the slogan: a skeptic cannot simply label a claim "extraordinary" and stop there. The skeptic must explain the relevant background knowledge, compare live alternative hypotheses, and say what sort of evidence would actually count for or against the claim.
Challenges to the Principle
Despite the strength of the Bayesian defence, challenges remain. One significant issue is the determination of prior probabilities. Priors need not be arbitrary; they can be shaped by frequency data, simplicity, explanatory power, background theories, and the reliability of the sources involved. But in large metaphysical questions, such as whether God exists or whether miracles are possible, the relevant background evidence is itself disputed. A naturalist and a theist may assign very different priors, not merely because one is biased, but because they differ over deeper explanatory commitments. That disagreement has to be addressed directly rather than hidden inside the word "extraordinary."
Furthermore, at the popular level the principle can be misapplied as a moving goalpost: whatever evidence is offered is declared not "extraordinary" enough. That is not how the serious academic version works. Careful philosophers of religion, including atheist or agnostic critics of theism such as Graham Oppy and Paul Draper, typically argue by comparing explanatory power, prior plausibility, and total evidence rather than by treating "extraordinary" as a magic word. The abuse of the slogan is therefore a real problem, but it should not be confused with the strongest version of the principle.
Additionally, "ordinary" and "extraordinary" are not two sharply separated boxes. They lie on a spectrum. Some claims are mildly surprising, some are deeply revisionary, and some are underdetermined because the evidence is still incomplete. This matters especially when science has an open question: an unsolved scientific problem should not be presented as proof of the supernatural, but neither should the mere possibility of a future natural explanation be treated as proof that a religious or metaphysical claim is false. The principle therefore requires careful, context-sensitive application.
Conclusion
In examining the maxim "extraordinary claims require extraordinary evidence," the fairest conclusion is that the principle is not self-defeating when understood carefully. Its strongest form is Bayesian: the less probable a claim is on our background knowledge, the stronger the evidence must be to make it reasonable to believe. That is a coherent rule of proportional belief, not an extraordinary empirical claim that must somehow pass its own test.
But the slogan is also dangerous when used loosely. It can conceal disputed priors, treat "not currently explained" as equivalent to "false," or demand a standard of evidence that no claim could satisfy. It also does not, by itself, establish atheism or refute theism. It only says that any worldview - theistic or atheistic - should proportion its confidence to the total evidence. Used with precision, the maxim is a helpful epistemic tool. Used as a conversation-stopper, it becomes rhetoric rather than reasoning.