I will conclude my survey of Part 1 of David Hume’s famous essay “Of Miracles” by proposing a better approach to the problem of miracles: that of Frank Ramsey and Bruno de Finetti.

To the point, Ramsey and de Finetti, building on the ideas of Thomas Bayes and Richard Price, developed a subjective theory of probability (see here and here). Broadly speaking, subjective probability represents an individual’s personal assessment of, or “degree of belief” in, the likelihood of an event happening or the truth of a proposition or hypothesis, e.g. that a given miracle really happened. In other words, whenever we estimate the probability of some event or proposition, our estimate is almost always based on our personal perceptions and experience, i.e. on gut feelings instead of formal calculations. So why not extend the concept of subjective probability as well as Bayesian reasoning more generally to reports of miracles?

Before proceeding any further, two digressions are in order. One is the relationship between subjective probability and political philosophy, for what I find most compelling about the idea of subjective probability is that it is consistent with the classical liberal ideal in favor of natural liberty: people have different beliefs about the world, and those beliefs should be tolerated — nay, celebrated! — so long as no one is harmed. My other digression is that one does not have to express one’s subjective probability or degree of belief in a miracle using numerical values. (See here, for example. See also John Maynard Keynes, Treatise on probability, Macmillan (1921), pp. 20-22.) It is sufficient to use such qualitative formulations as “highly likely, almost certain, or virtually impossible” to describe the likelihood of some event or proposition, given a body of evidence. (See James Franklin, “The objective Bayesian conceptualisation of proof and reference class problems,” Sydney Law Review, Vol. 33 (2011), pp. 545-561, especially pp. 547-548.)

In any case, once we accept the subjective nature of probability, we can easily apply Bayesian reasoning to miracles as follows: given a report of miracle M, you should assign a subjective probability value to the likelihood, however remote, that M really took place, and then you should incrementally update your subjective prior up or down as new evidence about M becomes available. (Moreover, my Bayesian approach to miracles is especially apt given that Bayes’s famous theorem may have originated in response to Hume’s argument against miracles!) For a step-by-step explanation of Bayesian reasoning, see my 2013 paper “Visualizing probabilistic proof” or my 2011 paper “A Bayesian model of the litigation game“. For now, however, I will conclude with one final observation: Bayes > Hume.