David Hume’s arguments against miracles succeed despite the fact he didn’t use Bayes’ Theorem. William Vanderburg briefly addresses this issue in his article for Hume Studies.[1] He shows Hume was aware of Bayes’ Theorem but didn’t think he needed it to make his argument.
Earman chastises Hume for being unaware of Bayesianism and of mathematical probability generally. This is unfair on two counts. First, Bayes’s work on probability was not widely known in 1748 when Hume published the first edition of the Enquiry. Richard Price arranged the posthumous publication of Bayes’s essay only in 1763, and it remained obscure even after its publication; Price’s paper applying Bayesian methods to the evidence for miracles appeared in 1767. We know Hume read and admired that paper, but he neither addressed Bayesian arguments nor revised his account of miracles for the 1768 and 1777 editions of the Enquiry. This suggests that Hume ultimately did not view Bayes’s work as relevant to the argument against miracles. Second, Hume’s discussion of the probability of chances “shows without controversy that he was familiar with the basic concepts of probability based on the calculus of chances.” Given Hume’s familiarity with Pascalian probability in general, and his acquaintance (through Price) with Bayesian ideas, his non-numerical treatment of the evidential probability of miracles must be seen as a deliberate philosophical position, not as a result of negligence or ignorance.[2]
What Hume is aiming at is seen in his general maxim: “Therefore we may establish it as a maxim, that no human testimony can have such force as to prove a miracle, and make it a just foundation for any such system of religion.” His twofold contention is not only that mere testimonial evidence for a miracle is insufficient for believing in a miracle, but also that miracles cannot be an adequate foundation for a religion. Hume is undercutting miracles and any religion born of miracles in one fell swoop. Going for the jugular vein of miracles does all the work, for it also deals a death blow to the religion of any miracle working god.
If miracles are the foundation for a religion, then an apologist for that religion cannot bring up a miracle working god to establish his supposed miracles. For miracles are supposed to be the basis for the religion and its miracle working god. One cannot reason backwards from the existence of their god to the miracle testimonies in the Bible. For the issue is whether the god of these miracles exists in the first place.
Apologists have only the testimonial evidence from ancient pre-scientific humans, without any relevant objective corroborating evidence. They cannot claim the Bible is divine testimony either, until they have established that the testimony in the Bible is good enough to establish its miracles. These are the kinds of problems Hume surely understood, which is why he didn’t bother with Bayes’ Theorem. And if this doesn’t explain why he didn’t use Bayes, it doesn’t matter. These same reasons are why no one needs to adopt Bayes when debating impossible events in the natural world like miracles, which have no prior data to work from, and no prior miracle working god who would do them.[3]
Apologists might start by first arguing for their god’s existence, but very few of them say, “Here is the objective evidence that our god exists.” They always seem to talk in terms of “presenting an argument” rather than “presenting the evidence,” which is very telling. So, an unevidenced god will not help an unevidenced miracle, just as an unevidenced miracle will not help an unevidenced god. The only thing apologists can do is special plead to their god and his religion by assuming what needs to be proved.
Just consider what apologists William Lane Craig and J.P. Moreland say about the hypothesis, “Jesus rose naturally from the dead.” They argue such a hypothesis is “fantastically, even unimaginably, improbable . . . given what we know about cell necrosis.”[4] In other words, they admit the evidence is woefully lacking to believe Jesus rose up from the dead without a miracle, or without a miracle working god, or without a miracle working god who would do such a miracle—that is, a Christian god. Got it! They need a miracle to believe Jesus rose from the dead. So therefore, that’s how they argue, backwards, from their prior belief in a miracle working god who would do such a miracle, to the miracle of the resurrection of Jesus. They do this because they realize that on natural grounds alone, they cannot make the case that a miracle like the resurrection took place. But if god comes first then whence comes god, the god of the resurrection? If the miracle of Jesus’ resurrection cannot be reasonably accepted unless the Christian god exists and raised him up from the dead, then where is the evidence for the god who raises Jesus up from the dead? The best explanation is that they just presuppose such a god due to cultural and familial influences, for if they didn’t already believe in the Christian god there would be no reason to think Jesus came back from the dead, because dead people stay dead.
--John W. Loftus. LINK to Book.
[In subsequent posts I'll discuss other reasons why Hume's lack of a response to Bayes is not "a result of negligence or ignorance" but "a deliberate philosophical position," per Vanderburgh.]
[3] I don’t object to using Bayes’ Theorem when applied appropriately to questions for which we have prior data to determine their initial probability. I do have objections to the use of Bayes’ Theorem when assessing miraculous events in the world which violate natural laws, where there is no prior data to work from. See my post, “Hypothesis: Since Bayes’ Theorem Cannot Help Us It Should be Abandoned” along with the tag below it, “Bayes’ Theorem.” LINK I know people disagree, that’s why I’m not making a big deal of it here.
[4] J. P. Moreland and William Lane Craig, Philosophical Foundations for a Christian Worldview (Downers Grove, IL: InterVarsity Press, 2003), 571.
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