Book review â€“ Proving History: Bayes's Theorem and the Quest for the Historical Jesus, by Richard Carrier. Prometheus Books, Amherst, 2012. ISBN 978â€“1â€“61614â€“560â€“6 (ebook)
This author, Dr. Richard Carrier PhD, is nothing if not ambitious: his aim is "to explore and establish the formal logic of all historical argument." Proving History
is the first of two volumes in which Carrier attempts to make the case that Jesus did not exist as an actual person. This first volume does not present that case but instead sets out to establish a methodology that can be applied in settling historical questions in general.
In the first chapter Carrier scoffs at the plethora of Jesuses, often wildly different from each other, that have been reconstructed by scholars on the basis of the same few historical sources. He considers the lack of consensus to be evidence that historians have been and are doing it wrong. Instead, writes Carrier, "[h]istorians must work together to develop a method that, when applied to the same facts, always gives the same result; a result all historians can agree must be correct." In an aside he then clarifies that to him "correct" means "the most probable result." It is somewhat unfortunate that the explicit statement of what is the central thesis of this book is tucked away between parentheses. In Carrier's view, historians should, when faced with alternative explanations, calculate their probabilities and pick the one with the highest outcome. If they do this properly, they will all get the same result.
The bulk of the book is, not unexpectedly in light of the above, concerned with probabilities, and in particular with a basic identity in probability theory known as Bayes's Theorem. More about this later. But what exactly is
a probability when referring to a historical event? It is fairly easy to grasp the meaning of "the probability of throwing 3 with an unbiased die is one sixth," because it concerns events that can be repeated at will. It is far less clear what is meant by "the probability that Jesus existed is 0.273," because we can't repeat history (Nietzsche notwithstanding). Unfortunately, Carrier is not particularly clear on his definition of probability. He makes the following half-hearted attempt in Chapter 2:
by â€œprobabilityâ€ here I mean â€œepistemic probability,â€ which is the probability that we are correct when affirming a claim is true. Setting aside for now what this means or how they're related, philosophers have recognized two different kinds of probabilities: physical and epistemic. A physical probability is the probability that an event x happened. An epistemic probability is the probability that our belief that x happened is true. For example, the probability that someone's uncle invented the global positioning system is certainly very small (since only a very few people out of the billions living on earth can honestly make that claim). But the probability that your belief â€œmy uncle invented the global positioning systemâ€ is true can still be very high. All it takes is enough evidence. The former is a physical probability, the latter an epistemic one.
This is hopelessly confused. First of all, there is no difference between "the probability that an event x happened" and "the probability that our belief that x happened is true." To see this, suppose that x is the statement "the outcome of a throw with a die is 3." The probability of our belief that a 3 was thrown being true is the same as the probability that a 3 was thrown. Considering that Carrier deals throughout with epistemic probabilities, it is especially frustrating that he is unable to provide an accurate definition.
Then there is the problem that "epistemic probability" is here defined as the "probability that etc.", which presumes that we already know what "probability" means (for the record, an epistemic probability is a degree of belief that event x occurred. It can be quite different from what Carrier calls the physical probability of that event. For example, if I suspect that the die has been tampered with, my epistemic probability that the outcome of a throw with a die is 3 can be different from one sixth).
In addition, the example given is a poor one, because in the first instance the event x is "someone's uncle invented the global positioning system," while in the second instance it morphed into "my uncle invented the global positioning system." These events are clearly not the same, as they should have been in a useful example.
In the final chapter Carrier reveals what is perhaps the source of his confusion, where he brazenly states that "[p]robability is obviously a measure of frequency." He then declares, "But what about epistemic probabilities? As it happens, those are physical probabilities, too. They just measure something else: the frequency with which beliefs are true." But this is plainly nonsensical. If I suspect that the tampered-with die will come up 3 with epistemic probability 0.21, then this does not necessarily measure the frequency with which the die will actually come up 3. At best it is a reasonable approximation.
At this point in Chapter 2 I considered throwing the book in the farthest corner, but realized just in time that I was reading an e-book on my laptop. The main substance of the chapter is not about probabilities anyway, but deals with twelve Axioms and an equal number of Rules which, in Carrier's opinion, should be accepted by all historians. The Axioms represent nothing less than "the epistemological foundation of rational-empirical history." To this reviewer, the axioms sound very much like something you would find on the website Less Wrong
â€“ in fact, the whole book with its gospel-like presentation sounds like something derived from the writings of that website's founder Eliezer Yudkowsky and his circle.
Axiom 1 states: "The basic principle of rational-empirical history is that all conclusions must logically follow from the evidence available to all observers." This is poorly worded ("the" evidence is almost never available to all observers, because some observers may have access to evidence that others do not), but otherwise uncontroversial. But Axiom 2 is already cringe-worthy: "The correct procedure in historical argument is to seek a consensus among all qualified experts who agree with the basic principle of rational-empirical history (and who practice what they preach)." Why should there be a consensus on topics where different, but about equally valid interpretations are possible? Is "agreeing to disagree" some kind of consensus too? Who are these qualified experts?
Other Axioms are merely redundant, such as Axiom 3: "Overconfidence is fallacious; admitting ignorance or uncertainty is not." In Axiom 1 we had agreed only to draw conclusions that logically follow from the evidence. That already excludes the kind of fallacious reasoning that Axiom 3 (again with heavy Less Wrong
overtones to me) warns against. I could go on: each of the other axioms is either a platitude, poorly worded, or redundant. How on earth can this random collection of admonishments be considered to be "the epistemological foundation of rational-empirical history"?
The twelve Rules, which Carrier "would like to see all historians consistently follow, in order to make their work more credible and worthwhile, and to make progress possible," are cut from the same cloth as the Axioms. Rule 6, for example, which basically tells us to keep Axioms 7 & 8 in mind, is implied by Rule 1, which states: "Obey [sic] the Twelve Axioms (given above) and Bayes's Theorem (articulated in the remainder of this book)." It all seems ad hoc and not properly thought through. Are these Axioms and Rules an exhaustive set? I doubt it.
In Chapter 3, Carrier introduces Bayes's Theorem. Those who have been taught Bayes's Theorem (BT) during an introductory course in probability theory will be surprised to learn what BT is.
In simple terms, Bayes's Theorem is a logical formula that deals with cases of empirical ambiguity, calculating how confident we can be in any particular conclusion, given what we know at the time.
Described in these, which I wouldn't call simple terms, BT appears to be potent stuff, sounding almost like a magical rather than a logical formula. This is strange, because all it really is is an elementary identity, relating a bunch of probabilities to each other. In its simplest form it can be derived from the axioms of probability theory in one or two lines of basic algebra.
Still, from this humble origin an impressive body of mathematical theory has arisen, which, under the proper conditions, provides a powerful set of tools for making inferences under uncertainty. The question is, can these tools be employed in the science of History to help settle questions such as "Did Jesus exist?" Carrier emphatically answers "yes", and in Chapter 4 even attempts to prove that all valid methods of History are "fully modelled and described by BT (and are thereby reducible to BT)." What he actually proves is that all methods that use probabilities in any way must be consistent with BT. Well, yes, that's because it is a theorem in probability theory. You can't work with probabilities while contradicting BT. This is trivially true. Nothing to prove here, people. Move on.
Much of the book goes into great, and frankly tedious, detail in treating some examples of calculating probabilities using BT. But what can BT actually do for historians?
All that BT does is to spit out a certain probability (let's call this P) when we feed it with a number of other probabilities ("priors"). This is often useful when it is difficult to calculate P directly, while we know how to calculate the priors. Now, suppose P is the probability that Jesus existed. In this case it should be clear that we are not dealing with ordinary (physical) probabilities, as in throwing a die. We are concerned with epistemic probability, degree of belief or uncertainty, whatever you want to call it. This implies that all the inputs into the formula, the priors, are also epistemic probabilities. So, where do they come from? It turns out, unfortunately, that they are often just as difficult to calculate as the probability of interest, P. Which is where the saying "Garbage In - Garbage Out" kicks in.
For all his bluster and pomposity, Carrier fails to show that the priors he needs to evaluate in order to answer a question like "Did Jesus exist?" can be calculated to any useful degree of accuracy. He basically pulls numbers from his posterior (what he calls a forteriori
reasoning). And this is where his programme fails. How can there ever be consensus among experts about the priors? He seems overly optimistic, as in waving the problem away, when he suggests that sharing of information and discussing the evidence will in the end necessarily lead to a consensus.
But we are not done yet. Carrier does not only believe he can transform the way historians should do their job. He even thinks he can do significant work in fundamental probability theory, for which he has no qualifications whatsoever. In his sixth and final chapter, Carrier claims that there is no essential difference between Bayesian and frequentist approaches to probability. He even believes that he has proved this assertion, thereby solving a longstanding problem that has baffled some of the finest mathematical minds. In the above I have already touched upon this topic, which in essence is about the difference between physical and epistemic probabilities. It is also a subject that has been treated thoroughly by another reviewer (Tim Hendrix
), who has shown that Carrier almost certainly did not understand what he was talking about (my paraphrase). This whole chapter smacks of someone seriously afflicted with a case of Dunning-Kruger expounding on subjects far above his grasp.
In summary, Bayesian methods may well have their use in Historical research. But this is not a book that is going to convince many historians, as it is evidently written by an incompetent amateur dabbling in topics way beyond his expertise. This is not taking into account that the author is known for being a lying sack of shit with delusions of grandeur.