Home » Library » Modern Library » Hume’s Maxim: How a “Trivial Truth” is Too Strong for Christian Apologetics

Hume’s Maxim: How a “Trivial Truth” is Too Strong for Christian Apologetics



In Hume’s Abject Failure, philosopher John Earman argues that David Hume’s famous maxim concerning the credibility of miracle reports amounts to no more than a trivial tautology, one that was already agreed upon by all parties to the 18th-century debate on miracles. A survey of contemporary Christian apologetic literature, however, reveals that even if Hume’s maxim was once obvious, it has been forgotten in modern times. In this paper I will first survey the attempts of contemporary Christian apologists to defend the miraculous resurrection of Jesus, and then demonstrate that all of these attempts fail to satisfy Hume’s purportedly obvious conditions.

Earman on Hume’s Maxim

In his essay “Of Miracles,” David Hume articulated his 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] In Hume’s Abject Failure, philosopher John Earman offers the following interpretation of Hume’s maxim: if M = the hypothesis that a particular miracle has occurred, t = testimony that M occurred, and K = our background knowledge, then Hume is saying that no testimony can establish M unless P(M|t&K) > P(~M|t&K), and therefore P(M|t&K) > .5.[2] That is, testimony cannot establish a miracle unless the testimony renders the miracle to be more probable than not. Thus, according to Earman, Hume’s maxim sets forth the following necessary and sufficient condition for accepting a miracle:

HM: one should not believe a miracle unless it is greater than 50% probable in light of the evidence.

When interpreted in this way, Hume’s maxim appears to be simple commonsense.[3] Of course testimony only can only establish a miracle if it makes that miracle probable! Who could possibly think otherwise? This is why Earman takes Hume’s maxim to be a trivial banality that no straight-thinking apologist would ever dispute in the first place. Some of Hume’s contemporary critics shared Earman’s sentiment. Consider George Campbell’s commentary:

What then shall be said of the conclusion which he [Hume] gives as the sum quintessence of the first part of the Essay? The best thing, for aught I know, that can be said is, that it contains a most certain truth, though at the same time the least significant, that ever perhaps was ushered into the world with such solemnity…. If any reader think himself instructed by this discovery, I should be loth to envy him the pleasure he may derive from it.[4]

In short, when Earman models Hume’s maxim in terms of conditional probabilities, the maxim appears to be no more than an unhelpful tautology. He thus concludes that Hume’s maxim contributes nothing to the philosophical literature on miracles, and is hardly deserving of the praise that it has received. But while Hume’s maxim may be an obvious banality to Earman, a quick reading of modern apologetic literature reveals that this is far from obvious to many of today’s primary defenders of Christianity. As we shall see, many apologists believe that Hume’s maxim is not a necessary condition for establishing a miracle. That is, they believe that testimony can establish a miracle even if P(~M|t&K) > P(M|t&K).

Licona’s Maxim

Christian historian Mike Licona has written a massive book titled The Resurrection of Jesus: A New Historiographical Approach, in which he seeks to establish the Resurrection on historical grounds. Licona’s methodology is abductive: he relies on the testimony of New Testament authors, primarily Paul, to make an inference to the best explanation in favor of the resurrection hypothesis. First, Licona identifies three “bedrock” historical facts:

  1. Jesus’ death by crucifixion.
  2. The disciples had experiences that they interpreted as appearances of the risen Jesus.
  3. The conversion of Paul.

Second, Licona compares six alternative explanations for these facts using five separate criteria: plausibility, explanatory power, explanatory scope, degree of ad-hocness, and illumination. Finally, Licona concludes that the Resurrection is the best explanation for these facts according to these five criteria.

In addition, Licona seems to think that because the Resurrection is the best of these explanations for these facts, then it is probably true. He writes: “[S]ince the resurrection hypothesis is the best explanation, fulfills all five criteria and outdistances all of its competitors by a significant margin, I contend that we may declare that Jesus’ resurrection is ‘very certain.'”[5] Formally, Licona’s argument is:

  1. Of the six hypotheses under consideration, the resurrection hypothesis is the best explanation for these three facts.
  2. The resurrection explanation meets all of the abductive criteria.
  3. The five other competing explanation fare much worse than the resurrection explanation.
  4. Therefore, the resurrection explanation is very certain.

Because 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. Recall that Hume’s maxim says that we should only accept a miracle when P(M|t&K) > .5. Licona seems to agree with this part of Hume’s maxim when he writes that an event should be only be considered “historical” if it is at least “probable” or “quite certain.”[6] And he clearly believes that the Resurrection can satisfy this condition of Hume’s maxim, because he thinks that the Resurrection is “very certain.” As Earman noted, another way of writing P(M|t&K) > .5 is P(M|t&K) > P(~M|t&K). This means that M must be more probable than the disjunction of every single alternative theory taken together. Thus, another way of writing Hume’s maxim is like this:

P(M|t&K) > [P(~M1|t&K) + P(~M2|t&K) + … + P(~Mn|t&K)]

Licona never considers whether M is more probable than ~M. Instead, he only asks how M fares against each of ~M’s subhypotheses taken individually. This is where Licona parts ways from Hume’s maxim. He thinks that he can establish that P(M|t&K) > .5 even if he cannot establish that P(M|t&K) > P(~M|t&K). Thus, Licona thinks that it is sufficient to show that each of the following is true:

P(M|t&K) > P(~M1|t&K)
P(M|t&K) > P(~M2|t&K)
P(M|t&K) > P(~M3|t&K)

P(M|t&K) > P(~Mn|t&K)

This approach, which we can call Licona’s maxim (LM), says that a miracle is “very certain”—i.e., P(M|t&K) > .5—if it is more probable than every competing explanation taken individually. LM is clearly a lower standard than HM, because a miracle can satisfy LM but still fail to satisfy HM. For this reason, LM is plainly false. It does not state a sufficient condition for establishing the probability of a miracle. We simply cannot establish that P(M|t&K) > .5 if we cannot establish that P(M|t&K) > P(~M|t&K).

Not only is this conclusion a trivial consequence of the probability calculus, but it jibes with our commonsense understanding of explanation. Philosopher Gregory Dawes writes: “The best available explanation may be so awful, so lacking in explanatory virtues, that we should not accept it, even if we have nothing better. In these circumstances, the most rational course of action would be to withhold acceptance while we see if we can find a more satisfactory alternative.”[7] Tim McGrew adds: “one might contest the implication that an explanation that is superior to its rivals in pairwise comparisons is actually more reasonable to believe than not. It is not difficult to imagine (or even to find) cases where one explanation is marginally better than any given rival but where the disjunction of the rival explanations is more believable.”[8] Similarly, Alvin Plantinga writes: “[Y]ou aren’t compelled by some rule of inference to accept a bad explanation of some phenomenon, even if that explanation is the best one you can think of. Suppose there are six candidates; suppose the most probable among them has a probability of .2. Even if that explanation is the best one, you will quite properly refuse to accept it as the truth of the matter.”[9]

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. This means that even if satisfying Licona’s maxim were sufficient to establish a miracle, Licona still hasn’t done enough work to establish that the Resurrection is “very certain.”

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 F1, F2, and F3. Thus, Licona’s book only compares P(M|F1&F2&F3) to five other alternative explanations also conditioned on F1, F2, and F3. But, of course, these three facts hardly exhaust what we know about the world. Suppose that there is a fourth fact F4 that is much more likely on an alternative hypothesis A than on M. In this case, P(F4|A) > P(F4|M), and therefore F4 raises the probability of A relative to M. And if the ratio of P(F4|A)/P(F4|M) is sufficiently large, then P(A|F1&F2&F3&F4) > P(M|F1&F2&F3&F4), in which case the Resurrection would no longer be the best explanation for the facts. Further, even if the ratio P(F4|A)/P(F4|M) is not large enough to tip the scales in favor of A, it is still possible that there are additional facts F5, F6, etc. that have the cumulative effect of making A the best explanation. In order to show that the resurrection hypothesis is the most probable explanation, Licona would either need to (1) show that there are no other relevant facts beside F1, F2, and F3, or (2) show that even if there are other facts that favor hypotheses beside the resurrection hypothesis, the evidential force of those facts is not strong enough to counteract the evidential force of F1, F2, and F3.

In sum, Licona’s book, even if successful, would only prove this: among a limited set of possible explanations for a limited set of data, the resurrection hypothesis has the highest individual probability. This does not exclude the possibility that:

  • the probability that some explanation other than the Resurrection is correct is greater than 50%, and therefore the Resurrection is probably false.
  • the Resurrection takes up less than half of the total probability space, even though it takes up the majority of the limited probability space that Licona investigates, and therefore the Resurrection is probably false.
  • there are other data that Licona does not consider that would drive the probability of the Resurrection below 50%, and therefore the resurrection is probably false.

After several hundred pages of heavy philosophical and exegetical lifting, this is not a very significant conclusion. The wide gulf between Licona’s claimed conclusion and his actual conclusion stems directly from the fact that he failed to take Hume’s advice and compare P(M|t&K) to P(~M|t&K).

The Craig-Davis Maxim

Apologist William Lane Craig strays even further from Hume’s maxim than Licona. Licona accepted the condition of Hume’s maxim that says P(M|t&K) must be greater than .5, but rejected the condition that P(M|t&K) must be greater than P(~M|t&K). Craig, on the other hand, recognizes that these conditions are identical, and therefore rejects them both. Thus, unlike Licona, Craig denies Hume’s maxim wholesale. He writes:

The successful Christian apologist need not show that the probability of the resurrection on the evidence and background information is higher than the probability of no resurrection on the same evidence and information. In other words, he need not show that the probability of the resurrection hypothesis is greater than 50 percent, or more probable than not. Rather, what he must show is that the probability of the resurrection is greater than any of its separate alternatives…. Thus, even if the resurrection hypothesis has a probability of, say, only 30 percent, and none of its alternatives scores higher than, say, 10 percent, then it is far and away the best explanation.[10]

Christian philosopher Stephen Davis has taken what is essentially the same view as Craig. Davis writes:

I do not accept [the] epistemological claim that the probability of a given hypothesis H must be greater than .5 for belief in H to be rational. Normally, this is indeed the case. But suppose we are in a situation where (a) there are four mutually exclusive alternatives to belief in H (call them A, B, C, and D); (b) each of A, B, C, and D has a probability of .15 (and thus the probability of the falsity of H is .6 and the probability of the truth of H is .4); (c) it is necessary to choose among H, A, B, and C; and (d) H, A, B, C, and D exhaust all the possibilities. In such a case, believing H is the most rational alternative.[11]

Thus, the Craig-Davis maxim (CDM) says that testimony is sufficient to establish a miracle if, for any alternative explanation An, P(M|t&K) > P(An|t&K), even if P(M|t&K) < .5. This is very clearly at odds with Hume’s maxim.

The claimed justification for the CDM is that ~M is not actually an explanation. It is merely the disjunction of many different explanations, so it is meaningless to say that ~M is the best explanation. This is all well and good, but the questions “what is the best explanation” and “what probably happened” address two separate issues, and it is the second question that we are interested in answering. The first question is only valuable insofar as it helps us answer the second. The CDM blurs this issue, and therefore it can lead a person to accept inconsistent beliefs. A person who accepts CDM may believe in the Resurrection as a historical event, but at the same time believe that the Resurrection is probably false. Perhaps Craig and Davis would respond by saying that “establish” according to the CDM merely means “establish as the best explanation” rather than “establish as a historical event.” But if this is the case, then there is no sense in which we can say that the testimony renders the miracle credible. Unless someone believes that a miracle probably happened, it is irrational to nonetheless simultaneously believe in it as a historical fact.

Imagine a 20-sided die that biased in favor of side 20. It lands on 20 1/5 of the time, and the other 19 sides are equally probable. If you had to bet on a single number, 20 would be the best bet. But if you had the bet on whether it will land on 20 or not land on 20, you should obviously bet against 20. Similarly, if the Resurrection is the best explanation, then the resurrection is the best individual option. But if we had to bet on whether the Resurrection is true or false, we should still bet against it.

Davis is correct to say that when we have five separate options, it is rational to pick the most probable option, even if it is less than 50% probable. But this is only true when two conditions are met. First, we must know all of the possible options, which is never the case in historical scholarship. Second, Davis’ approach is only rational when, in his words, “it is necessary to choose among” the options. In this case, the justification for choosing the most probable option is purely pragmatic. If we are forced to choose, it is wisest to choose the option with the highest probability of being correct. We simply have no other choice. We choose the best option, not because we think it is correct, but because our hand has been forced and it is the most prudent choice. But note, this is a purely pragmatic reason for affirming the truth of a miracle, not an epistemic one, and Craig and Davis claim to believe in the Resurrection on the grounds that it is epistemically, rather than prudentially, justified.

It should be noted that it is not entirely clear whether or not Craig actually thinks the CDM is enough to warrant belief in a miracle. In his review of the philosopher Jordan Howard Sobel’s defense of Hume’s argument, Craig criticized Sobel for interpreting Hume’s maxim as P(M|K) > P(t&~M|K). Craig rejects this standard for miracle credibility because “this alone is just not significant in determining whether a miracle has occurred”[12], for it is merely a necessary, but not a sufficient, condition for showing that P(M|t&K) > .5. Here, Craig is essentially arguing that we should adopt Hume’s original maxim that miracles should only be believed if they are more probable than not. If this is so, then Craig should reject his own maxim, which merely proposes a necessary condition for P(M|t&K) > .5.

The Craig-Moreland Maxim

In The Blackwell Companion to Natural Theology, Craig, along with philosopher J. P. Moreland, endorses an even less stringent maxim for miracle acceptance. As the editors of the book, Craig and Moreland summarize the chapter by the philosophers Timothy McGrew and Lydia McGrew in the following way:

They [the McGrews] argue that in the case of Jesus’s putative resurrection, the ratio between the likelihoods of the resurrection hypothesis and its contradictory is such that one ought to conclude that the resurrection hypothesis is the most probable hypothesis on the total evidence.[13]

Notice how, as above, Craig and Moreland think it is enough to demonstrate that the Resurrection is “the most probable hypothesis” rather than “probably true.” I have already outlined the problems with this approach above. Here I aim to show that Craig and Moreland’s criteria for determining whether a hypothesis is “the most probable” is invalid. For background, the McGrews argue for the Resurrection by identifying 3 pieces of information that they think are more likely on the hypothesis that the Resurrection (R) happened than on the hypothesis that it did not. These are:

(W): The discovery of the empty tomb by Jesus’ women followers.
(D): The disciples’ claims to have seen Jesus after his death.
(P): The conversion of Paul.

From here, the McGrews argue that P(W&D&P|R) > P(W&D&P|~R). That is to say, that R has greater predictive power with respect to these facts than ~R. Craig and Moreland seem to think that on the basis of this inequality, we can infer that R is the most individually probable hypothesis. But this is a non sequitur. Even if this condition is satisfied:

P(select pieces of evidence|H) > P(select pieces of evidence|~H)

It does not follow that each of the following is true:

P(H|total evidence) > P(~H1|total evidence)
P(H|total evidence) > P(~H2|total evidence)
P(H|total evidence) > P(~H3|total evidence)

P(H|total evidence) > P(~Hn|total evidence)

This inference, which I will call the “Craig-Moreland maxim,” is the most fallacious and egregious deviation from Hume’s maxim that we have seen thus far. In stark contrast to Craig and Moreland, the McGrews recognize that they cannot infer that the Resurrection is probable, or even the most probable hypothesis, on the basis of their argument. The McGrews write:

To show that the probability of [the resurrection] given all evidence relevant to it is high would require us to examine other evidence bearing on the existence of God, since such other evidence—both positive and negative—is indirectly relevant to the occurrence of the resurrection. Examining every piece of data relevant to R more directly—including, for example, the many issues in textual scholarship and archeology which we shall discuss only briefly—would require many volumes. Our intent, rather, is to examine a small set of salient public facts that strongly support [the resurrection].[14]

Note the modesty of the McGrews’ argument. They merely claim that a few select pieces of evidence make the Resurrection more probable than it otherwise would have been. They recognize that in order to say that a miracle is probable, one must follow Hume’s maxim and compare P(M|t&K) to P(~M|t&K), or in this case, P(R|total evidence) to P(~R|total evidence). Anything less will necessarily result in a weaker conclusion. In the spirit of charity, we can assume that Craig and Moreland have simply misspoke, or were perhaps commenting on an earlier draft of the McGrews’ paper.


In his essay “Of Miracles,” Hume lays out a set of conditions that must be met before concluding that testimony renders a miracle believable. He argues that the miracle must be more probable than not, and that this is only true if it is more probable that the miracle occurred than that it did not occur. In Earman’s eyes, Hume was merely stating a simple tautology. However, Hume’s maxim is clearly far from obvious to many of today’s leading Christian apologists. Earman may think that Hume’s maxim was so self-evident that it didn’t need to be said, but as we have seen, it still needs to be said more than 250 years later. Thus, 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.


[1] David Hume, An Enquiry Concerning Human Understanding (1748), Ch. 10, para. 13.

[2] John Earman, Hume’s Abject Failure: The Argument Against Miracles (New York, NY: Oxford University Press, 2000), p. 41.

[3] Earman, Hume’s Abject Failure, p. 42.

[4] Cited in Earman, Hume’s Abject Failure, p. 42. Others have challenged Earman’s construction of Hume’s maxim and offered interpretations that are less straightforward, but that escape Earman’s charge that Hume’s maxim is a mere banality. For example, see Peter Millican, “Hume, Miracles, and Probabilities: Meeting Earman’s Challenge,” a paper presented at the Hume Conference, Las Vegas, NV, July 2003. <http://www.davidhume.org/papers/millican/2003%20Hume%20Miracles%20Probabilities.pdf>. I will here assume for the sake of argument that Earman’s interpretation is correct.

[5] Michael R. Licona, The Resurrection of Jesus: A New Historiographical Approach (Downers Grove, IL: InterVarsity Press, 2010), p. 619.

[6] Licona, The Resurrection of Jesus, pp. 124-125.

[7] Gregory W. Dawes, Theism and Explanation (New York, NY: Routledge, 2009), p. 24. Of course, Licona might quibble that the resurrection hypothesis fulfills the requirements of all of his explanatory virtues, but Dawes’ general point about abductive reasoning is otherwise applicable.

[8] Timothy J. McGrew, “Miracles” in The Stanford Encyclopedia of Philosophy (Fall 2015 edn.) ed. E. N. Zalta (Stanford, CA: Stanford University, 2009). <https://plato.stanford.edu/archives/fall2015/entries/miracles/>.

[9] Alvin Plantinga, Where the Conflict Really Lies: Science, Religion, and Naturalism (New York, NY: Oxford University Press, 2011), p. 223.

[10] William Lane Craig, “Responses” in Five Views on Apologetics ed. Steven B. McGowan (Grand Rapids, MI: Zondervan, 1999), p. 126.

[11] Stephen T. Davis, “The Counterattack of the Resurrection Skeptics: A Review Article.” Philosophia Christi Vol. 8, No. 1 (2006): 39-63, p. 42.

[12] William Lane Craig, “Sobel’s Acid Bath for Theism: A Review Essay of Jordan Howard Sobel’s Logic and Theism.” Philosophia Christi Vol. 8, No. 2 (2006): 481-490.

[13] William Lane Craig and J. P. Moreland, “Introduction” in The Blackwell Companion to Natural Theology ed. William Lane Craig and J. P. Moreland (Malden, MA: Blackwell, 2009): ix-xiii, p. xiii.

[14] Timothy McGrew and Lydia McGrew, “The Argument From Miracles: A Cumulative Case for the Resurrection of Jesus of Nazareth” in The Blackwell Companion to Natural Theology ed. William Lane Craig and J. P. Moreland (Malden, MA: Blackwell, 2009): 593-662, p. 595.

Copyright ©2017 Aron Lucas. The electronic version is copyright ©2017 by Internet Infidels, Inc. with the written permission of Aron Lucas. All rights reserved.