In the previous post we began to discuss the fundamental difference between the Bayesian and frequentist approaches to probability. A Bayesian defines probability as a subjective belief about the world, often expressed as a wagering proposition. “How much am I willing to bet that the next card will give me a flush?”

To a frequentist, however, probability exists in the physical world. It doesn’t change, and it isn’t subjective. Probability is the hard reality that over the long haul, if you flip a fair coin it will land heads up half the time and tails up the other half. We call them “frequentists,” because they maintain they can prove that the unchanging parameter is fixed and objectively true by measuring the frequency of repeated runs of the same event over and over.

Fairies and witches

But does objective probability really exist? After reading several books focused on subjective probability published in the past few decades, I couldn’t help noticing that Bruno de Finetti‘s Theory of Probability stands as a kind of watershed. In the preface he says that objective probability, the very foundation of frequentism, is a superstition. If he’s correct, that means it isn’t just bad science; it’s anti-science. He writes: read more »

Thanks to a reader who has alerted me to an article by a philosopher of history, Aviezer Tucker, on Richard Carrier’s Proving History in the prestigious peer-reviewed journal History and Theory. I have since seen an rss feed alerting me to Carrier’s own comments on the review. I look forward to reading it but meantime I’d like to remind readers of a post I did a few years ago on the author:

I also see that Tucker’s review has been made open access. (The journal’s policy is to make a work open access if the author or their supporting institution pays a fee of $3000. So do appreciate the access you have to this article. It’s free to you but the publisher is not giving it away free.)

Richard Carrier addresses two online criticisms of his book, Proving History: Bayes’s Theorem and the Quest for the Historical Jesus, in a new blogpost, Understanding Bayesian History.

I took time out from my own chapter by chapter reviews of the book to read a history of Bayes’ Theorem by Sharon McGrayne, The Theory That Would Not Die. I’d like to return to discussions of Bayes’ rule with that additional reading background. One thing that stands out from reading the way Bayes’ theorem has been successfully applied and the social and political struggles it has had for open acceptance (it has much more often been covertly accepted) until today is that the more complexities and nuances their are impinging upon any question, the more appropriate is the use of Bayes’ theorem to help resolve them. That means that those arguments that history is too complex for Bayes to be of use fail to understand that it is complexity and nuance of so many unknown quantities that Bayes assists us in handling. McGrayne’s book also shows us that some of the arguments used against Bayes today are identical to the ones that were used long ago until they were eventually proven unfounded.

Carrier is responding to criticisms by an atheist-mathematician-with-New-Testament-interests on Irreducible Complexity.

Richard Carrier writes:

When Ian isn’t ignoring the refutations of his own arguments in the very book he’s critiquing, he is ignoring how applications of Bayes’ Theorem in the humanities must necessarily differ from applications in science (again for reasons I explain in the book), or he is being pointlessly pedantic and ignoring the fact that humanities majors need a more colloquial instruction and much simpler techniques than, for instance, a mathematical evolutionist employs.

Over on New Oxonian, Hoffmann is at it again. In “Proving What?” Joe is amused by the recent Bayes’ Theorem (BT) “fad,” championed by Richard Carrier. I’ll leave it to Richard to answer Joe more fully (and I have no doubt he will), but until he does we should address the most egregious errors in Hoffmann’s essay. He writes:

So far, you are thinking, this is the kind of thing you would use for weather, rocket launches, roulette tables and divorces since we tend to think of conditional probability as an event that has not happened but can be predicted to happen, or not happen, based on existing, verifiable occurrences. How can it be useful in determining whether events ”actually” transpired in the past, that is, when the sample field itself consists of what has already occurred (or not occurred) and when B is the probability of it having happened? Or how it can be useful in dealing with events claimed to be sui generis since the real world conditions would lack both precedence and context?

I must assume that Joe has reached his conclusion concerning what he deems to be the proper application of Bayes’ Theorem based on the narrow set of real-world cases with which he is familiar. He scoffs at Carrier’s “compensation” that would allow us to use BT in an historical setting:

Carrier thinks he is justified in this by making historical uncertainty (i.e., whether an event of the past actually happened) the same species of uncertainty as a condition that applies to the future. To put it crudely: Not knowing whether something will happen can be treated in the same way as not knowing whether something has happened by jiggering the formula.

Different values yield different answers!

I’m not sure what’s more breathtaking: the lack of understanding Hoffmann demonstrates — a marvel of studied ignorance — or the sycophantic applause we find in the comments. Perhaps he’s getting dubious advice from his former student who’s studying “pure mathematics” (bright, shiny, and clean, no doubt) at Cambridge who told him:

Its application to any real world situation depends upon how precisely the parameters and values of our theoretical reconstruction of a real world approximate reality. At this stage, however, I find it difficult to see how the heavily feared ‘subjectivity’ can be avoided. Simply put, plug in different values into the theorem and you’ll get a different answer. How does one decide which value to plug in?

You don’t have to do very much research to discover that Bayes’ Theorem does not fear subjectivity; it welcomes it. Subjective probability is built into the process. And you say you’re not sure about what value to plug in for prior probability? Then guess! No, really, it’s OK. What’s that? You don’t even have a good guess? Then plug in 50% and proceed.

It’s Bayes’ casual embrace of uncertainty and subjectivity — its treatment of subjective prior probability (degree of belief) — that drives the frequentists crazy. However, the results speak for themselves.

And as far as getting different answers when you plug in different numbers, that’s a common feature in equations. Stick in a different mass value in F = ma, and — boom! — you get a different value for force. It’s like magic! Good grief. What do they teach at Cambridge these days?

The proper application of BT forces us to estimate the prior probabilities. It encourages us to quantify elements that we might not have even considered in the past. It takes into account our degree of belief about a subject. And it makes us apply mathematical rigor to topics we used to think could be understood only through intuition. Hence BT’s imposed discipline is extraordinarily useful, since we can now haggle over the inputs (that’s why they’re called variables) rather than argue over intuitive conclusions about plausibility — because truthfully, when a scholar writes something like “Nobody would ever make that up,” it’s nothing but an untested assertion.

I saw none of the other apostles, except James the brother of the Lord. — Galatians 1:19

On this verse some hang their strongest assurance that Jesus himself was an historical figure. Paul says he met James, the brother of the Lord (assumed to be Jesus), so that is absolute proof that Jesus existed. That sounds like a perfectly reasonable conclusion. So reasonable, in fact, that some quickly denounce as perverse cranks any who deny this “obvious meaning”.

But should historians be content with this? Is it being “hyper-sceptical” to question this explanation?

We need to keep in mind some fundamental principles of historical research and explanations from the professional historians themselves. Renowned conservative historian, Sir Geoffrey Elton, warns against deploying such simplistic methods as citing a single piece of evidence to make a case. In this instance, the case is about evidence for the historicity of Jesus.

Historical research does not consist, as beginners in particular often suppose, in the pursuit of some particular evidence that will answer a particular question (G.R. Elton, The Practice of History, p.88)

If that’s what historical research is not, Elton goes on to explain what it is:

it consists of an exhaustive, and exhausting, review of everything that may conceivably be germane to a given investigation. Properly observed, this principle provides a manifest and efficient safeguard against the dangers of personal selection of evidence. (p.88)

Since I am currently reading and reviewing Richard Carrier’s Proving History: Bayes’s Theorem and the Quest for the Historical Jesus I am taking time out in this post to see what happens if I test this “obvious” interpretation of Galatians 1:19 by means of Bayesian principles. Carrier argues that Bayes’ Theorem is nothing more than a mathematical presentation or demonstration of what goes on inside our heads when we are reasoning about any hypothesis correctly. So let’s try it out on the conclusions we draw from Galatians 1:19.

The way it works is like this. (But keep in mind I am a complete novice with Bayes’ theorem. I am trying to learn it by trying to explain what I think I understand so far.) I see a verse in Paul’s letters that appears to have a simple explanation. I think of myself as a geologist looking at strata in a rock face and I think about all I know about strata and the evidence in front of me and with all that in mind I try to work out how that strata came to look the way it does. This verse is like that strata. My task is to test a hypothesis or explanation for how it came to be there and to appear as it does.

So the explanation, or hypothesis, that I decide to test is: That James, whom Paul meets according to this letter, was a sibling of Jesus. That’s my initial explanation for this verse, or in particular this phrase, “James the brother of the Lord”, being there.

It seems pretty straightforward, surely. This should be easy enough to confirm.

So let’s set it out in the theorem structure. read more »

I have been studying the first half of Richard Carrier’s chapter 3, “Introducing Bayes’s Theorem”, in his recent book Proving History: Bayes’s Theorem and the Quest for the Historical Jesus. I mean studying. I want to be sure I fully understand the argument before tackling the second half of the chapter, headed Mechanics of Bayes’s Theorem, which promises to be “the most math-challenging section of the book” (p. 67). Maths is not my most outstanding strength so I want to be sure I get the basics clear before moving into those waters. I have come to a point where I can enjoy playing little mind-games with Bayes’ Theorem for the sake of reinforcing my understanding. Last night on the TV news was dramatic story of an unexpected resignation of a leading Australian political figure. So I found myself piecing all I heard, how I heard it and what I knew etc. into a Bayes’ equation and calculating the probability that the story was true. Kind of fun. At least for the moment before the novelty factor wears off.

Result: While I believe I can see Richard’s point some of my niggling questions have not yet gone away.

When did the sun go out?

Carrier begins by setting out our reasoning when we read in the Gospels that darkness covered the whole earth for three hours at the time of the crucifixion of Jesus. What he is seeking to do is to take readers through the processes they would undergo in order to conclude that such an event almost certainly never really happened.

To make the scenario work he posits at least a barely conceivable natural cause for the event: “a vast dense cloud of space-dust swiftly drifting through the plane of the solar system . . .” — Wouldn’t the Sun’s gravity prevent that? But I’m happy to go along with the exercise for sake of argument nonetheless.

The critical point for Carrier is that what would convince us that such an event really had happened in the past is if we could find records testifying of the event across all world cultures thousands of miles apart from Britain to China.

There could not fail to have been mention or discussion of such a remarkable and terrifying event across many of these cultures among their surviving textual traditions and materials. (p. 43).

The key point is that we know in advance that this is the evidence we would expect to find IF such an event had happened.

And if indeed that were the case, we would surely have adequate warrant to believe the sun was blotted out for three hours on the corroborated day . . .

What Carrier is preparing his readers for is to accept that reasoning about historical events is fundamentally similar to reasoning in the sciences. If such and such a hypothesis (or explanation) is true then we would predict (or expect) certain events (or evidence) to be manifest.

Then there is the converse. If such a hypothesis (explanation) were true, we would NOT expect to find a universal silence in the surviving records:

[A] single claim in a single religion repeated only in its own documents (and documents relying on those), is extraordinarily improbable — unless the event was entirely made up. . . . This is a slam-dunk Argument from Silence, establishing beyond any reasonable doubt the nonhistoricity of this solar event . . . (p. 44)

My niggling question:

I follow the reasoning. But in my mind, rather than taking me into the realm of mathematics, it all leads back to my own argument about how historians know anything at all about the persons and events of the past. read more »

Here Carrier pauses before addressing Bayes’ theorem in order to establish fundamentals that ought to be part of the basic mechanics of every historical enquiry.

The first subsection of the chapter is “Why History Requires Expertise”. Carrier opens by listing three golden rules he always offers lay people who ask him what history they can trust:

Don’t believe everything you read;

Always ask for the primary sources of a claim you find incredible;

Beware of scholars who make amazing claims but who are not experts in the period or even historians.

I have learned to extend #2 to “always ask for the primary sources of all claims — including the commonplace ones”. read more »

Till now I’ve always been more curious than persuaded about Carrier’s application of Bayes’s Theorem to what he calls historical questions, so curiosity led me to purchase his book in which he discusses it all in depth, Proving History: Bayes’s Theorem and the Quest for the Historical Jesus.

Before I discuss here his preface and opening chapter I should be up front with my reasons for having some reservations about Carrier’s promotion of Bayes’ theorem. (Allow me my preference for Bayes’ over Bayes’s.) I should also say that I’d like to think I am quite prepared to be persuaded that my resistance is a symptom of being too narrow-minded.

My first problem with Carrier’s use of the theorem arises the moment he speaks of it being used to “prove history” or resolve “historical problems”. For me, history is not something to be “proved”. History is a quest for explanations of what we know has happened in the past. Historical problems, to my thinking, are problems having to do with how to interpret and understand what we know has happened in the past. The milestone philosophers of the nature of history — von Ranke, Collingwood, Carr, Elton, White — have certainly spoken about history this way.

I have always understood that where there is insufficient data available then history cannot be done at all. Ancient history, therefore, does not allow for the same sorts of in-depth historical studies as are available to the historian of more recent times. Historical questions are necessarily shaped (or stymied altogether) by the nature and limitations of the available sources.

Criteriology (I take the term from Scot McKnight‘s discussion of the historical methods of biblical scholars in Jesus and His Death) has always looked to me like a fallacious attempt to get around the problem of having insufficient data to yield any substantive answers to questions we would like to ask. We don’t know what happened? Okay, let’s apply various criteria to our texts to see if we can find out what “very probably really did happen”.

Carrier’s introduction of Bayes’ theorem has always appeared to me to be an attempt to salvage some value from a fundamentally flawed approach to “history” — the striving to find enough facts or data with which to begin to do history.

I should add that I do like Carrier’s offering of hope that Bayes’ theorem can promote more rigorous and valid thinking and applications of criteria. But I can’t help but wonder if in the end the exercise is an attempt to patch holes in the Titanic with admittedly very good quality adhesive tape.

What is really accomplished if we find only a 1% probability for the historicity of Jesus? Improbable things really do happen in the world. Otherwise we would never know chance and always be living with certainty. Or maybe I’m overlooking something about Carrier’s argument here.

Not that I’m a nihilist. I do believe we have lots of useful evidence to assist us with the study of Christian origins. I think scholars are agreed that pretty much all of that evidence speaks about a Christ of faith (a literary figure) and not an historical figure. That’s where our historical enquiry must begin — with the evidence we do have. After we analyse it all and frame such questions as this sort of evidence will allow us to ask then we can begin to seek explanations for Christian origins. This will probably mean that we will find answers that do not address the life and personality of someone who is hidden from view. Our understanding will address religious developments, ideas, culture, literature, social developments. We will probably be forced to conclude — as indeed some historians do — that if there is an historical Jesus in there somewhere he is irrelevant to our enquiry.

So that is where I am coming from.

Let’s see if I am being too narrow-minded. Here is my reading of Carrier’s preface and opening chapter. read more »

I’d like to thank you for this very nice representation of what I was trying to show in the book. It’s always gratifying when a reader zeroes in on exactly those aspects I thought were most interesting and most central to my argument. Thank you for this careful and engaged reading of my work – much appreciated!
— Eva Mroczek, June 2017

I think you have a high quality blog that provides a positive public service by discussing academic topics within a wider audience.
— Russell Gmirkin, October 2016

Very good. This post is going straight to the March 2016 Biblical Studies Carnival. — N.T. Wrong, March 2016

For an excellent example of generally high-quality scholarship by someone who isn’t a biblical studies professor, see Neil Godfrey’s work posted on the website vridar.org.
— Tom Dykstra, JOCABS 2015

Neil Godfrey and Tim Widowfield, who both write at Vridar . . . happen to be some of the most astute and well-read amateurs you can read on the internet on the subject of biblical historicity. I call them amateurs only for the reason that they don’t have, so far as I know, advanced degrees in the subject. But I have often been impressed with their grasp of logic and analysis of scholarship. I don’t always agree with them, but I respect their work.
— Richard Carrier, March 2014

Thanks for your very elaborate review! I realized that I hadn’t added your blog to our blogroll. This oversight has been corrected. Looking forward to more segments.
— Anthony Le Donne, September 2009

I always enjoy reading Neil’s blog because I think that he is careful, thorough, intellectually fair, and honest.
— April DeConick, November 2007

Neil Godfrey on Scholarly Snobbery and Wikipedia (again): “My god I think you are right! And I trusted a biblical scholar to be honest about what he was…” Aug 18, 10:20

db on Scholarly Snobbery and Wikipedia (again): “The embedded image from above is not a screen-shot of a Wikipedia article, but rather a Google Search page.…” Aug 18, 09:10

On the Historicity of Jesus: “Neil Godfrey: I seriously think that you should submit this series of blog posts (or at least this one especially)…” Aug 19, 11:39