David Hume settled this centuries ago: a miracle is a violation of a law of nature established by the uniform experience of all humanity, and it will always be more probable that the testifier is mistaken or lying than that the law of nature was actually suspended. No testimony can ever be strong enough to justify believing a miracle occurred.

Why people find it persuasive

Hume's argument in An Enquiry Concerning Human Understanding is a genuinely powerful piece of philosophy: it appeals to our everyday practice of weighing competing improbabilities, and it explains why we are right to be skeptical of modern miracle claims from faith healers and cult leaders, which gives it real intuitive traction before it is even applied to the biblical accounts.

Important distinctions

• • Uniform experience defined as what always happens vs. defined circularly as what happens absent miracles
• • A priori argument that miracles cannot be credible vs. a posteriori case-by-case evaluation of specific testimony
• • Laws of nature as descriptive regularities vs. laws as metaphysically necessary and inviolable
• • Hume's argument against believing in miracles vs. an argument against miracles occurring at all

Christian response

• • The core problem, identified by philosophers including C.S. Lewis in Miracles and more rigorously by contemporary philosophers like John Earman in Hume's Abject Failure, is that Hume's argument is circular. To say uniform experience is against miracles, one must already have established that every purported miracle report in history is false; but that is precisely the question at issue, so uniform experience cannot be invoked as an independent premise without begging the question against any particular reported exception.
• • Hume also conflates two different things: how often an event of a given type occurs in the ordinary course of nature, which is indeed vanishingly rare for something like resurrection, and whether, on a particular occasion, there is good reason to think something outside the ordinary course occurred, including because of who is claimed to have caused it. If a God who created the laws of nature exists, it is entirely coherent that this same God could occasionally act in ways that transcend those regularities without those regularities failing on any other occasion, similar to how an author's typical style does not prevent an atypical scene written on purpose.
• • Bayesian analyses of Hume's argument, done by philosophers such as Richard Swinburne and John Earman, show that the strength of testimony needed to make a miracle report more probable than not depends on the antecedent probability of the miracle, which in turn depends on background metaphysical questions like whether God exists and would have reason to act in the situation described. Hume's argument treats this prior as fixed at essentially zero by definition, which only follows if naturalism is already assumed to be true, making the argument dependent on the very conclusion it is meant to establish independently.
• • Historically, Hume's essay was extremely influential rhetorically but is now regarded by many philosophers of religion, including non-theists, as logically flawed in its strongest form; even the philosopher Antony Flew, before his later shift toward theism, acknowledged that Hume's argument shows only that miracle testimony needs to be very strong, not that it can never in principle be strong enough. This is an important concession that shifts the debate back to the specific historical evidence rather than settling it by philosophical fiat.

Christian counterresponse

The theist would respond that this is now a much weaker and more reasonable claim than Hume's original, one requiring case-by-case historical evaluation of the specific testimony's reliability rather than an a priori dismissal, and once the argument is recast this way it becomes an empirical historiographical debate that can be engaged rather than an argument that settles the matter before the evidence is examined.