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.








