A dead man rising, a virgin birth, a universe with a beginning caused by a mind, these are extraordinary claims, and extraordinary claims require extraordinary evidence. Ordinary historical testimony, of the kind we would accept for a mundane event, is not enough to justify believing something that violates everything we know about how the world works.

Why people find it persuasive

The principle, popularized by Carl Sagan as extraordinary claims require extraordinary evidence, captures something intuitively correct: we rightly demand more from claims of alien abduction or perpetual motion machines than from claims that someone had lunch yesterday, because the prior improbability of the claim must be overcome by the evidence's strength.

Important distinctions

• • Bayesian prior improbability vs. claims being extraordinary merely because they are unfamiliar or metaphysically loaded
• • The strength of evidence needed vs. the type of evidence that counts
• • Applying the standard evenhandedly vs. applying it only to religious claims
• • Miracle claims embedded in a theistic framework vs. miracle claims in an assumed naturalistic framework

Christian response

• • The Sagan standard is really a restatement of Bayes's theorem: the amount of evidence needed to justify belief in a hypothesis is inversely proportional to that hypothesis's prior probability. This is correct as a piece of general epistemology, but it smuggles in a hidden premise when applied to miracles, namely that the prior probability of an event like the resurrection must be assessed on the assumption that no God exists who might act in history. If a Creator plausibly exists, a separate question to be argued independently through cosmological or fine-tuning arguments, then the prior probability of an occasional divine act in history is not nearly as low as the prior probability of a law of physics randomly failing.
• • Historian and philosopher Timothy McGrew and others have pointed out that the extraordinary evidence standard is often applied inconsistently: historians accept single, non-corroborated ancient testimony for countless mundane facts about antiquity, yet demand a wholly different evidential category, sometimes effectively unfalsifiable, for miracle claims specifically. If the evidential bar is raised so high that no possible historical evidence could ever meet it, the objection has stopped being an evidential principle and become a methodological exclusion of the supernatural by definition, which is philosophy, not history.
• • It is also worth being precise about what extraordinary evidence the resurrection claim actually has: multiple independent early sources, including Paul's creed in 1 Corinthians 15, dated by most scholars including skeptical ones to within a few years of the event, the transformation of the disciples from a scattered, fearful group into people willing to die for their testimony, the conversion of a hostile figure like Paul, and the empty tomb tradition attested even in polemical responses by opponents. This is a convergence of multiple independent lines rarely available for ancient events, which is a legitimate form of extraordinary evidence even if it is not a video recording.
• • A fair-minded skeptic like Bart Ehrman, who denies the resurrection, nonetheless agrees that the disciples sincerely believed they saw the risen Jesus and that this belief, not a later legend, is the earliest layer of tradition; the live scholarly debate is over how to explain that experience, not whether extraordinary testimony of some kind exists. This shows the objection, properly understood, shifts the conversation from there is no real evidence to here is competing evidence about how to interpret the evidence there is, which is a much more modest and defensible claim than the slogan suggests.

Christian counterresponse

The theist can note this proves too much, since it would rule out believing any miracle report a priori regardless of evidence, making the position unfalsifiable by definition rather than a genuinely evidential stance, and Hume's own argument faces exactly this circularity charge from philosophers like John Earman.