Bayesian reasoning is widely used in a range of scientific disciplines. According to the GP Margaret McCartney, for example, Bayesian reasoning is "a good description of how medicine is practised" (The Patient Paradox: Why Sexed Up Medicine is Bad for Your Health). Historians, however, have yet to discover the delights of Bayes's Theorem, and Richard Carrier wants that to change. In this important book Carrier pursues two related objectives: "first, to demonstrate when and why existing methods of historical reasoning are valid; and second, to provide a model of reasoning that can be directly employed in historical analysis and argument. The latter is methodological, the former is epistemological."
For those historians who baulk at what appears to be a purely scientific methodology, and one that involves a daunting-looking equation, Carrier points out that many sciences such as geology and cosmology are in fact historical, in the sense that they "explore not merely scientific generalizations but historical particulars, such as when the Big Bang occurred". Indeed, much of science involves field observations and doesn't rely on experiments. "History is thus continuous with science. The difference between them is only quantitative: history must work with much less data, of much less reliability."
Every time we say that some event is "implausible" or "unlikely" we are "covertly making a mathematical statement of probability" - whether or not that is what we think we are doing. (In Believing in Magic: Psychology of Superstition, the psychologist Stuart Vyse makes a similar point: "Much of our day-to-day thinking is quantitative, whether we are aware of it or not.") Carrier tabulates a canon of probabilities, with five percentages on either side of "even odds" that range from "virtually impossible" to "virtually certain" (both one in a million) and include "very improbable" and "very probable" (both one in twenty). Thus he links familiar verbal descriptions with their underlying numbers, emphasizing the probabilistic nature of historical knowledge.
Judgements about degrees of belief reflect the uncontroversial fact that ignorance and uncertainty are hallmarks of good scholarship in any discipline. In history, as in science, very little is known for sure, and confidence must often be measured in relative degrees of certainty. Historians learn to avoid black-and-white terms like "true" and "false" and to be comfortable with ambiguity, uncertainty and ignorance (just like scientists, according to Firestein in Ignorance: How It Drives Science). This state of affairs is tailor-made for Bayes's Theorem, which can be formulated as a theory of warrant rather than of truth: it tells us what we are warranted in believing, not what is true in any absolute sense.
One sign of poor scholarship - and a common failure of critical thinking - is eagerness to adopt a particular explanation just because it "fits the evidence". Many explanations will fit (in fact, an infinite number are logically possible), but not all are equally believable. Working out the probability that our hypothesis is true (in the language of Bayes) entails not only examining "the specific evidence that requires explanation" (which our hypothesis purports to explain), but also taking into account any relevant background knowledge ("everything all historians know or should be able to know") and all the significant alternative hypotheses. Bayes's Theorem shows that the probability that our hypothesis is true follows necessarily from four other probabilities (technically, the prior and consequent probabilities).
One huge advantage of Bayes over the historicity criteria that have "so dismally failed" is that the theorem has been proved and is therefore logically valid. The maths represents a logic that "models the structure of all sound historical reasoning". (Logic matters, since invalid arguments can never reliably produce true conclusions; see, for example, Rulebook for Arguments. Logic is also no respecter of departmental boundaries, even if some corners of the academy are less respectful of logic than they should be.)
In a short first chapter Carrier outlines the central problem that bedevils attempts to get to the "real" historical Jesus (the method of criteria), the consequences of the failure of this methodology (a more confused picture of Jesus), and the solution (Bayes's Theorem). A second chapter covers the basics, the set of methodological assumptions to which all historians should subscribe, and a third introduces Bayes's Theorem. The core of the book comprises two chapters on the Bayesian analysis of historical methods and criteria, in which Carrier aims to show both the limitations of some aspects of the existing methodology and the power of the Bayesian approach. For example, the criterion of coherence ("the most insidious of them all") "assumes that anything that coheres with what has been established with other criteria is also historical." The problem here is that good fiction is often just as "coherent" as historical fact. Indeed, it can be even more so, for coherence is easy to create by design, and "is just as common and expected on hypotheses of fabrication."
The most egregious example of historians using the same method on the same facts to get a whole range of different results is in Jesus studies. For Carrier, this shows that the method of criteria "is invalid and should be abandoned" and he insists that "agreement on the fundamentals of method is the first essential requirement for any community of experts to deem itself an objective profession." To this end he proposes that professional historical inquiry should be based on a set of core epistemological assumptions: the twelve axioms of historical method that "represent the epistemological foundation of rational-empirical history." For good measure, there are also twelve rules all historians should follow. Again, axioms and rules may seem alien in a subject like history, but many of these will already be familiar to historians, and to anyone with a grounding in critical thinking (for example, the eleventh axiom invalidates cherry-picking and special pleading and other abuses of logic and evidence).
In Did Jesus Exist?: The Historical Argument for Jesus of Nazareth, Bart Ehrman relies heavily on the method of criteria (for example, "the criterion of dissimilarity") to establish his conclusion that the historicist position is right and the mythicist position wrong. While Carrier does not fully address the historicity of Jesus here (he will do that in a forthcoming volume), he does undermine the consensus position: "the many contradictory versions of Jesus now confidently touted by different Jesus scholars" cannot all can be true, but they can all be false. And if they are all false, does that mean there never was a historical Jesus?
Carrier offers three basic rules to laypeople who ask him what history to trust: "(1) don't believe everything you read; (2) always ask for the primary sources of a claim you find incredible; and (3) beware of scholars who make amazing claims about history but who are not experts in the period". As a layreader, I confess that I found the book tough going in places (nearly a third is taken up with the final chapter, ominously called "The Hard Stuff"). For the professional historian, however, "it's too hard" is not an excuse we should ever hear, "because mastering difficult methods is what separates professionals from amateurs." In one important respect, however, Bayes's Theorem should make the historian's life easier, since it brings into the open unstated assumptions and so facilitates the resolution of disagreements.
Only cranks and crackpots challenge the ability of science to understand the world around us. So why is history, which is the study of the world no longer around us, so firmly rooted in the humanities? Few historians will dispute Carrier's claim that they "need solid and reliable methods" and that their arguments must be logically valid and factually sound. (Those that do dispute this claim ought to pack up and become historical novelists instead.) Although Carrier makes a good case for Bayes's Theorem to be taken seriously by historians, it remains to be seen whether they will embrace Bayes with any enthusiasm. What does seem certain is that Bayesian reasoning will help us to see more clearly into our past, and that this book will help historians see more clearly the value of Bayes's Theorem.