Category Archives: Bayes’ Theorem

What’s the Difference Between Frequentism and Bayesianism? (Part 2)

by Tim Widowfield

Witch of Endor by Nikolay Ge

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 »

What’s the Difference Between Frequentism and Bayesianism? (Part 1)

by Tim Widowfield

English: Picturing 50 realisations of a 95%-confidence interval (Photo credit: Wikipedia)

As my thesis partner and I gathered up the evidence we had collected, it began to dawn on us — as well as on our thesis advisers — that we didn’t have enough for ordinary, “normal” statistics. Our chief adviser, an Air Force colonel, and his captain assistant were on the faculty at the Air Force Institute of Technology (AFIT), where my partner and I were both seeking a master’s degree in logistics management.

We had traveled to the Warner Robins Air Logistics Center in Georgia to talk with a group of supply-chain managers and to administer a survey. We were trying to find out if they adapted their behavior based on what the Air Force expected of them. Our problem, we later came to understand, was a paucity of data. Not a problem, said our advisers. We could instead use non-parametric statistics; we just had to take care in how we framed our conclusions and to state clearly our level of confidence in the results.

Shopping for Stats

In the end, I think our thesis held up pretty well. Most of the conclusions we reached rang true and matched both common sense and the emerging consensus in logistics management based on Goldratt’s Theory of Constraints. But the work we did to prove our claims mathematically, with page after page of computer output, sometimes felt like voodoo. To be sure, we were careful not to put too much faith in them, not to “put too much weight on the saw,” but in some ways it seemed as though we were shopping for equations that proved our point.

I bring up this story from the previous century only to let you know that I am in no way a mathematician or a statistician. However, I still use statistics in my work. Oddly enough, when I left AFIT I simultaneously left the military (because of the “draw-down” of the early ’90s) and never worked in the logistics field again. I spent the next 24 years working in information technology. Still, my statistical background from AFIT has come in handy in things like data correlation, troubleshooting, reporting, data mining, etc.

We spent little, if any, time at AFIT learning about Bayes’ Theorem (BT). I think looking back on it, we might have done better in our thesis, chucking our esoteric non-parametric voodoo and replacing it with Bayesian statistics. I first had exposure to BT back around the turn of the century when I was spending a great deal of time both managing a mail server and maintaining an email interface program written in the most hideous dialect of C the world has ever produced. read more »

Bayes, Schizophrenia, Autism and Brain Chemistry

by Neil Godfrey

A fascinating essay, even if speculative, by Scott Alexander on the brain chemistry behind Bayesian, deductive and inductive reasoning, and light it possibly sheds on conditions like schizophrenia, autism, and being stoned.

It’s Bayes All The Way Up

What Does “Probably” Mean to Historians and Forecasters?

by Neil Godfrey

We often hear it said that historians deal with probabilities, not certainties. Thus Bart Ehrman explains in his latest book:

Historians, of course, can ask what probably happened in the past, for example, in the earthly ministry of Jesus with his disciples. And historians can establish with relative levels of probability that this, that, or the other tradition is likely something that happened or didn’t happen. But history is all a matter of such greater or lesser probabilities. When dealing with a figure such as Jesus, these probabilities are established only by critically examining the memories that were recorded by later authors.

Ehrman, Bart D. (2016-03-01). Jesus Before the Gospels: How the Earliest Christians Remembered, Changed, and Invented Their Stories of the Savior (p. 31). HarperCollins. Kindle Edition. [My bolded emphasis in all quotations.]

Interestingly Ehrman assumes as a certainty (not probability) that the gospel narratives were sourced from “memories” of Jesus (whether personally experienced or fabricated memories) and sidesteps an entire area of biblical scholarship that argues the evangelists themselves imaginatively created the narratives of Jesus inspired by analogous tales in the Jewish Scriptures and other writings. He also uses the language — e.g. “that were recorded by” — we associate with historical “reports” or “records” thus further entrenching his bias in the mind of the reader. But we’ll leave Ehrman’s own contradictions aside for now and focus on the more general principle.

Anyone who has read scholarly works relating to Christian origins is familiar with the language of probability, possibility, maybe, likelihood, etc. Too often, however, this same language magically transforms itself as the argument proceeds into certainty. As Jacob Neusner in Rabbinic Literature and the New Testament complained of “pseudocritical” scholarship, it is commonly characterized a number of faults including

the use of “presumably,” “must” or “may have been,” and “perhaps,” a few sentences later magically converted into “was” and “certainly.” (p. 88)

A serious possibility

Let’s start with the reverse of history: forecasting the future. The past is past and gone but reverse our perspective for a moment and problems with vague and loose language become immediately obvious. The following cases are taken from Superforecasting: The Art and Science of Prediction by Philip E. Tetlock and Dan Gardner. In early 1951 the CIA published a National Intelligence Estimate warning that a Soviet Union attack on Yugoslavia “should be considered a serious possibility.” What does that phrase mean to you?

But a few days later, Kent was chatting with a senior State Department official who casually asked, “By the way, what did you people mean by the expression ‘serious possibility’? What kind of odds did you have in mind?” Kent said he was pessimistic. He felt the odds were about 65 to 35 in favor of an attack. The official was startled. He and his colleagues had taken “serious possibility” to mean much lower odds. Disturbed, Kent went back to his team. They had all agreed to use “serious possibility” in the NIE so Kent asked each person, in turn, what he thought it meant. One analyst said it meant odds of about 80 to 20, or four times more likely than not that there would be an invasion. Another thought it meant odds of 20 to 80— exactly the opposite. Other answers were scattered between those extremes.

Tetlock, Philip; Gardner, Dan (2015-09-24). Superforecasting: The Art and Science of Prediction (Kindle Locations 858-864). Random House. Kindle Edition.

A fair chance

When in 1961 President Kennedy sought to know the chance a small army of Cuban expatriates landing at the Bay of Pigs would have in toppling Fidel Castro his Chiefs of Staff concluded that the plan had a “fair chance” of success.

The man who wrote the words “fair chance” later said he had in mind odds of 3 to 1 against success. But Kennedy was never told precisely what “fair chance” meant and, not unreasonably, he took it to be a much more positive assessment.

Tetlock, Philip; Gardner, Dan (2015-09-24). Superforecasting: The Art and Science of Prediction (Kindle Locations 872-873). Random House. Kindle Edition.

Sherman Kent of the CIA’s Office of National Estimates sought a remedy by setting out more precise meanings: read more »

A Historian Reviews Carrier: “The Bayesian perspective on historiography is commonsensical”

by Neil Godfrey

Aviezer Tucker

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:

Real Historians Do Bayes!

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.)

More Thoughts on Minimal Historicity: When Bigger Isn’t Better

by Tim Widowfield

U-2 over California

Many years ago, I had what I still consider the best job in the world. A second lieutenant in my twenties, I found myself in charge of operational maintenance on the swing shift for the entire “black side” of the flightline at Beale Air Force Base. Back then, the tankers were on the north side of the flightline, while the U-2s (including their TR-1 cousins) and SR-71s sat on the south side.

Of course, the real work depended on experienced NCOs. As the old joke goes, the job of an OIC (Officer in Charge) is to listen to the NCOIC, then nod and say, “Oh, I See.” But I did serve at least one crucial function. Only an officer could sign off on a “Red X” and clear a plane to fly.

One night we were driving around in the little blue pickup truck assigned to the maintenance officer on duty, when we stopped at one of the U-2 shelters. The senior NCO and I were checking on the status of some repair; I forget exactly what it was now. At any rate, we got to talking and one of the guys asked the crew chief about a car he’d been looking at. The young buck sergeant told us that he did almost buy one vehicle. It looked nice, he said, and the payments seemed reasonable. But then he noticed something fishy.

“When I added up all the payments,” he said, “it was more than the price of the car!”

I felt compelled to explain. “If . . . I mean . . . Suppose . . . Hmm.” And then I realized there wasn’t enough time to explain how interest works, and it wasn’t clear it would do much good anyway. I gave a wide-eyed look at the senior NCO, offered some excuse about needing to get over to the SR-71s, and we quickly departed.

I had a similar feeling of helplessness reading Dr. Matthew Baldwin’sA Short Note on Carrier’s ‘Minimal Historicism.'” One’s first inclination is to want to help someone who’s thrashing about wildly, but where to start? Baldwin writes in his post, “This game is more than somewhat suspect: it is rigged from the start.” And he followed up with the same sentiments in his comment on Neil’s recent post, where he wrote: read more »

Ten Elements of Christian Origin

by Neil Godfrey

Richard Carrier addresses the question of the historicity of Jesus in On the Historicity of Jesus: Why We Might Have Reason for Doubt in the following order:

First, he defines the points that will identify a historical Jesus and those that will be signs of a mythical one.

Second, he set out 48 elements that make up all the background information that needs to be considered when examining the evidence for Jesus.

Third, only then does he address the range of evidence itself and the ability of the alternative hypotheses to account for it.

What Carrier is doing is enabling readers to think through clearly the different factors to be assessed in any analysis of the question: the details of the hypotheses themselves, our background knowledge (none of it must be overlooked — we must guard against tendentious or accidental oversights) and the details of the evidence itself. The book thus sets out all the material in such a way as to enable readers to think the issues through along the following lines:

— given hypothesis X, and given our background knowledge, are the details of this piece of evidence what we would expect? how likely are these details given hypothesis X and our background knowledge?

and (not “or”)

— are the details of this particular evidence what we would expect given the alternative hypothesis (and all our background knowledge)? how likely are these details given our alternative hypothesis and our background knowledge?

That, in a nutshell, is what his Bayesian analysis boils down to. The point of the assigning probability figures to each question and simply a means of assisting consistency of thought throughout the entire exercise. (At least that’s my understanding.)

I’ll put all of this together in a more comprehensive review of Carrier’s book some time in the not too distant future, I hope.

Meanwhile, I’d like to comment on the first ten of his background elements: those of Christian origins. read more »

The Argument from Design Meets a Third Contender, and Bayes

by Neil Godfrey

William Paley

In crossing a heath, suppose I pitched my foot against a stone and were asked how the stone came to be there, I might possibly answer that for anything I knew to the contrary it had lain there forever; nor would it, perhaps, be very easy to show the absurdity of this answer.

But suppose I found a watch upon the ground, and it should be inquired how the watch happened to be in that place, I should hardly think of the answer which I had given, that for anything I knew the watch might have always been there.

Yet why should not this answer serve for the watch as well as for the stone; why is it not admissible in that second case as in the first?

For this reason, and for no other, namely, that when we come to inspect the watch, we perceive — what we could not discover in the stone — that its several parts are framed and put together for a purpose, e.g., that they are so formed and adjusted as to produce motion, and that motion so regulated as to point out the hour of the day; that if the different parts had been differently shaped from what they are, or placed in any other manner or in any other order than that in which they are placed, either no motion at all would have carried on in the machine, or none which would have answered the use that is now served by it. (William Paley, Natural Theology, p. 1)

William Paley’s famous argument for creation by a designer consists of two distinct arguments joined together:

• Artefacts like watches and living organisms like eyes have special functions. Watches to tell the time; various kinds of eyes to see in various types of environments: “each such entity exists because of its function” (p. 42);
• Such functionality implies a designer both conscious and intelligent.

Biologists accept the first argument.

The second proposition seems right given the axiom that a cause must precede every effect. The effect is the ability to see. It must therefore follow that the eye was caused to exist for this specific function. In other words we have a teleological argument for the existence of eyes. They appeared for the purpose of enabling sight.

According to Paley there are only two alternatives. A complex organism, such the eye, must have come about either by

1. a conscious designer

or

2. blind chance aided by no other mechanism

Real Historians Do Bayes!

by Neil Godfrey

How do historians, comparative linguists, biblical and textual critics, and evolutionary biologists establish beliefs about the past? How do they know the past?

Aviezer Tucker

That’s the subject of Aviezer Tucker‘s Our Knowledge of the Past: A Philosophy of Historiography (2004). Tucker’s interest is the relationship between the writing of history (historiography) and evidence (p. 8). It is written for audiences interested in philosophy, history, biblical criticism, the classics, comparative linguistics and evolutionary biology (p. 22).

When I began to review Richard Carrier’s book, Proving History, I pointed out that far from substituting crude mathematics for historical inquiry, the application of Bayes’ Theorem merely expresses in symbolic terms the way historians evaluate the nature of evidence and test hypotheses to explain evidence for certain events and artefacts. Some fearful critics have objected to the application of Bayes because they have never understood this fact.

All Bayes’ theorem does is help us clarify our thinking. Bayes theorem is simply a symbolic way of expressing how we do our best thinking when seeking explanations for evidence or evaluating hypotheses against the evidence. The more complex the factors that need to be considered in addressing a problem the easier it is for us to overlook a critical point or draw invalid comparisons. Bayes’ helps us to clarify thinking about the most complex of issues, including those in the social sciences and history. *

Why Bayes?

Tucker writes as a philosopher and concurs with the above assessments of other authors addressed in my earlier posts. Philosophers like to clarify the complexities they are discussing and are apt to use illustrative symbols to this end.

Philosophers find often that formal representation, Bayesian probability in our case, clarifies and concentrates the discussion. Some historians and many classicists may not be as used to this form of representation as their philosophical colleagues. . . . When I use formal representation, I express the same concepts in words, for the benefit of readers who are not accustomed to formal notation. (p. 22)

Historians ask questions like the following:

To what degree does a piece of evidence contribute or not to the confirmation of a hypothesis, given background conditions? (p. 96)

Specifically:

To what extent does a similar saying in the Gospels of Matthew and Luke support, or not support, the Q hypothesis, given everything else we know that is relevant to the question?

To what extent does the passage “born of a woman” in Galatians 4:4 support, or not, the hypothesis that the author believed Jesus was an historical person in the recent past, given everything else we know about Galatians, that verse in particular and its context, and evidence for Jesus?

The Bayesian theorem purports to state formally the relation between a particular piece of evidence and the hypothesis. (p. 96)

In the fifty or so pages of chapter 3 Tucker demonstrates

that an interpretation of Bayesian logic is the best explanation for the actual practices of historians. (p. 96) read more »

Hoffmann Serf-Reviews My Bayes’ Theorem Post, “Proving This!”

by Tim Widowfield

Gentleman Joe (Photo credit: Wikipedia)

Gentleman Joe

Over on The New Oxonian, R. Joseph Hoffmann, leader of the Jesus Process©™® Triumvirate has deigned to comment on my post, “Proving This! — Hoffmann on Bayes’ Theorem.” As expected, his response is both cordial and understated. Ever the gentleman, he remains humble, even though Hoffmann’s massive and mighty brain threatens to burst through his shiny, pink forehead. At first I had considered answering him right there on his site. However, since I respectfully disagree with so much of what he has written, I have decided to create a new post here on Vridar instead.

I’ll quote chunks of Hoffmann’s words here, interspersed with my responses.  He’s reacting to a comment by a guy who goes by the screen name “Hajk.” Hoffmann begins:

Yes @Hajk: I was laughing politely when Vridar/Godfey[sic] made the bumble about “pure mathematics” in scare quotes; it reveals that he is a complete loser in anything related to mathematics, and when he goes on to complain that Bayes doesn’t “fear subjectivity it welcomes it” may as well toss in the towel as far as its probative force goes. Odd, someone conceding your points and then claiming victory.

Proving This! — Hoffmann on Bayes’ Theorem

by Tim Widowfield

Alan Mathison Turing: Genius, Computational Pioneer, and BT Fan (Photo credit: Garrettc)

Misunderstanding a theorem

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.

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.

Bayes’ Theorem ascendant

If you can possibly spare the time, please watch the video after the page break. In it, Sharon Bertsch McGrayne, author of The Theory That Would Not Die: How Bayes’ Rule Cracked the Enigma Code, Hunted Down Russian Submarines, and Emerged Triumphant from Two Centuries of Controversy recounts the story of how Bayes’ Theorem won the day. She tells us how BT is well suited for situations with extremely limited historical data or even no historical data — e.g., predicting the probability of the occurrence of an event that has never happened before. read more »

Putting James the Brother of the Lord to a Bayesian Test

by Neil Godfrey

spelt out in blue neon at the offices of Autonomy in Cambridge. (Photo credit: Wikipedia)

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 »

Carrier’s “Proving History”, Chapter 3(a) — Review

by Neil Godfrey

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 »

Richard Carrier’s “Proving History: Bayes’s Theorem and the Quest for the Historical Jesus” Chapter 1 (A Review)

by Neil Godfrey

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 »