Philosopher Michael P. Levine writes a bit eccentrically about miracles but he also has some incisive things to say. For people who think David Hume’s arguments against miracles are obsolete and should be ignored, Levine says, “The locus classicus for modern and contemporary philosophical discussion of miracles is Chapter X (‘Of Miracles’) of David Hume’s Enquiries.”[1] [“Locus classicus is a Latin term used in literature, law, and other academic fields. It refers to the original or most authoritative passage or source for a particular word, phrase, concept, or idea. In other words, it is the classical or standard example that is most often cited as the definitive reference for a subject.”] So he proceeds to analyze what Hume wrote.
He tells us “there are various versions of Bayes’s theorem,” not just one, depending on the hypothesis to be resolved. With miracles they are many. He highlights John Earman’s formulation:
“The reader is invited to think of H as a hypothesis at issue; K as the background knowledge; and E as the additional evidence. Pr(H/E&K) is called the posterior probability of H. [i.e., the Probability of the Hypothesis divided by the background Knowledge]. Whereas Pr(H/K) and Pr(E/H&K) are respectively called the prior probability of H and the (posterior) likelihood of E.”[2]
Labeling this as “Hume’s argument” Levine adds:
On the interpretation of Hume’s argument given above, a Bayesian analysis sheds no light whatsoever on the structure or substance of the argument, and can do nothing by way of either supporting or refuting the argument. Indeed, any Bayesian analysis of the question of justified belief in miracles must be otiose until the difficult and essential questions concerning “evidence” in relation to an allegedly miraculous occurrence are resolved - at which point any Bayesian analysis will add little except the technical complexity of a formal apparatus that may or may not “clarify” the structure of Hume’s argument. The balancing of probabilities is of no use until it is decided what goes into the balance - that is, what constitutes the evidence.[3]
Let's Highlight the Evidence (E). This is the crucial factor regardless of one’s background knowledge (K) or priors. Regarding a Christian Bayesian analysis, Levine comments, “The idea that the Bible provides historically acceptable grounds for believing in miracles reflects a wish-fulfilling rendering of what constitutes evidence.”[4] Everything hangs on the quantity and the quality of the evidence. It’s the indispensable input, the essential element, and the non-negotiable necessity.
First Case to Consider) Aaron Lucas’ Paper. (J.D. Georgetown University Law Center, 2016). See his paper: Hume’s Maxim: How a “Trivial Truth” is Too Strong for Christian Apologetics at The Secular Web/August 3, 2017.
Lucas highlights David Hume’s famous maxim that “That 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.”[1] That is, human testimony cannot establish that a miracle occurred unless the testimony renders the miracle to be more probable than not. But critic John Earman claims Hume’s maxim says “one should not believe a miracle unless it is greater than 50% probable in light of the evidence.” That's not what Hume says. So according to Earman, Hume’s maxim "appears to be no more than an unhelpful tautology." He concludes "it contributes nothing to the philosophical literature on miracles, and is hardly deserving of the praise that it has received." But Lucas goes on to argue "modern apologetic literature reveals that [even if this is the case] this is far from obvious to many of today’s primary defenders of Christianity."
For the record, Earman grossly misinterpreted Hume. In part one “Of Miracles” Hume’s argument is that in order to reasonably conclude that a miracle took place, an event must have an utterly overwhelming amount of strong human testimony to overcome our experience of the normal daily operation of the laws of nature, in which miracles don’t occur. Given our daily experience of the laws of nature it’s not reasonable to accept human testimony that a miracle took place, as it never amounts to an utterly overwhelming amount of strong human testimony. The very best that human testimony could show on behalf of a miraculous event is to equal, or match, our daily experiences from the laws of nature against it. But if it’s possible this testimonial burden could be met we should suspend our judgment, since at best, matching equals cancel each other out. So even this remote possibility is not enough for reasonable people to believe in miracle reports.[5]
Nonetheless, Lucas goes on to argue that many apologists, including Michael Licona, William Lane Craig, and J.P. Moreland, also misunderstand or mischaracterize Hume's maxim. Lucas:
Licona’s approach attempts to do an end run around Hume’s maxim, it fails for at least three reasons. The first flaw is that even if the Resurrection really were the best explanation, this, in itself, would not warrant the belief that the Resurrection is “very certain.” It is possible for an explanation to be the best explanation, fulfill all of these criteria, and surpass all other explanations by a significant margin, but still probably be false.
The second flaw in Licona’s argument is that although he says that the resurrection hypothesis is the best explanation, he really only means that it is the best of the explanations he considers in his book. He only considers five others. These five hypotheses obviously don’t take up 100% of the probability space. If one hypothesis is the best among a set of hypotheses that only make up a portion of the total probability space, it does not follow that it is the best explanation. There could still be explanations that Licona hasn’t considered that are better than the Resurrection.
The third flaw in Licona’s argument is that he only considers a limited set of data. Instead of assessing the probability of the Resurrection in light of all the relevant evidence, he narrows the evidence down to the three bedrock facts [mentioned].
Contrary to Earman, who claimed Hume’s maxim was an obvious tautology, Lucus says it is “clearly far from obvious to many of today’s leading Christian apologists.” So “if Hume is to be faulted for stating the obvious, many of today’s leading Christian thinkers should be faulted all the more for failing to see the obvious.”
Second Case to Consider) William Lane Craig.[6]
Like Licona, Craig thinks that it’s good enough to demonstrate the Resurrection of Jesus is merely “the most probable hypothesis” rather than “probably true.” This, Lucas shows us, is “a fallacious and egregious deviation from Hume’s maxim.”
The problem with Craig is significant. He tries to make a distinction between how he knows Christianity is true from how he shows others that Christianity is true. He says he knows Christianity is true by a (holy) spirit guide, just as a psychic knows s/he has been contacted by “the other side.” When it comes to showing Christianity is true, Craig uses philosophical arguments for the existence of his God, along with alleged testimonial evidence for the resurrection of Jesus from the dead. In other words, Craig admits his attempts to show Christianity is true are all a sham, a ruse, a mere debating tactic just to win for show, since he, along with every other Christian, already knows Christianity is true by a spirit guide.[7]
Craig says he knows the miraculous events in the Bible happened because of the witness of a (holy) spirit guide. Craig says this witness is “self-authenticating.” What does he mean by that? “I mean that the witness, or testimony, of the Holy Spirit is its own proof; it is unmistakable; it does not need other proofs to back it up; it is self-evident and attests to its own truth.” Hitchhiking on the philosophical work of Alvin Plantinga’s defense of a properly basic belief in God,[8] and quote-mining the Bible (e.g., John 14:16-26; 16:7-11; Galatians 3:26; 4:6; 8:15-16; 1 John 2:20,26-27; 3:24; 5:7-10), Craig writes: “I would agree that belief in the God of the Bible is a properly basic belief, and emphasize that it is the ministry of the Holy Spirit that supplies the circumstance for its proper basically. And because this belief is from God, it is not merely rational, but definitely true.”
Craig says he knows Christianity is true not because of any historical evidence. He writes:
In considering the historical evidence for the resurrection of Jesus, it is important to avoid giving the impression that the Christian faith is based on the evidence for Jesus’ resurrection. The Christian faith is based on the event of the resurrection. It is not based on the evidence for the resurrection.
This distinction is crucial.
The Christian faith stands or falls on the event of the resurrection. If Jesus did not rise from the dead, then Christian is a myth, and we may as well forget it. But the Christian faith does not stand or fall on the evidence for the resurrection.
Craig explains:
If we insist on a historical, evidential foundation for faith, then we consign most of the world’s population to unbelief. To me this is unconscionable. Therefore, if one’s religious beliefs are to be rational, there must be some other basis for them than the evidence. We are therefore not dependent on historical proofs for knowledge of Christianity’s truth. Rather through the immediate, inner witness of God’s Holy Spirit every person can come to know the truth of the Gospel once he hears it. Through an existential encounter with God Himself every generation can be made contemporaneous with the first generation of believers.
Craig cites the Bible as the ultimate authority on this, concluding:
The Bible says all men are without excuse [Romans 1]. Even men who are given no good reason to believe and many persuasive reasons to disbelieve have no good excuse, because the ultimate reason they do not believe is that they have deliberately rejected God’s Holy Spirit. Therefore, the role of reason in knowing Christianity is true is to be a servant. A person knows Christianity is true because the Holy Spirit tells him it is true, and while reason can be used to support this conclusion, reason cannot overrule it.
Therefore, Craig concludes:
It is never an appropriate response to defeaters to abandon Christian faith and reject Jesus Christ and the witness of the Holy Spirit. Rather, God can be trusted in such circumstances where we feel at a loss as to how to answer the defeater and we have no extrinsic defeater of the defeater, God can be counted on to so intensify the witness of the Holy Spirit that that will enable us to have an intrinsic defeater-defeater so that the appropriate response is to continue to believe with the hope that someday we may, in fact, find an error in that defeater and be able to expose its falsehood. The witness of the Holy Spirit is an intrinsic defeater-defeater.
To see just how deep he goes, Craig says, “I am asserting that not only should I continue to have faith in God on the basis of the Spirit’s witness even if all the arguments for His existence were refuted, but I should continue to have faith in God even in the face of objections which I cannot at that time answer.” So any attempt by him to use Bayes’ Theorem is a cover-up for “priors” that are set at 100% in his head, evidence be damned.
Third Case to Consider) The Video by Brian Blais and YouTuber Paulogia. Dr. Blais is a Professor in the Department of Biological and Biomedical Sciences at Bryant University. They did an excellent video titled, “What Bayes’ Theorem Really Says About the Resurrection” (August 2025).[9] When apologist Than Christopoulos accused YouTuber Paulogia of “mathematical malpractice” for his skepticism, Paulogia enlisted physicist and statistical inference expert Brian Blais. This video features Dr. Blais’s detailed breakdown of the debate, where he corrects the Bayesian equations, reframes the data, and argues that the apologist’s own math reveals a conclusion baked in from the start, turning a theological debate into a fascinating lesson on logic and probability. The “Maximal Data Case” for the resurrection of Jesus by Christopoulos is shown to be a sophisticated argument “for the Bible tells me so.” This video is how to use Bayes’ Theorem correctly.
[1] Michael Levine, “Philosophers on Miracles” in Graham H. Twelftree, ed., The Cambridge Companion to Miracles (Cambridge University Press, 2011), p. 302.
[2] Levine, “Bayesian Analyses of Hume’s Argument Concerning Miracles” at https://plato.stanford.edu/archives/fall2001/entries/miracles/#Bay
[3] Levine, Ibid.
[4] Michael Levine, “Philosophers on Miracles” in Graham H. Twelftree, ed., The Cambridge Companion to Miracles (Cambridge University Press, 2011), p. 299.
[5] See https://infidels.org/library/modern/questioning-miracles/#main
[6] From my paper, Psychic Epistemology: The Special Pleading of William Lane Craig
[7] References for this section are found at https://infidels.org/kiosk/article/psychic-epistemology-the-special-pleading-of-william-lane-craig/
[8] See Plantinga, Warranted Christian Belief (Oxford, UK: Oxford University Press, 2000).
[9] https://www.youtube.com/watch?v=v6QenX4Oo78 or at https://youtu.be/v6QenX4Oo78?si=UhYzC8Hy59BTvvho
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