My review of Richard Carrier's "On the Historicity of Jesus"

[shunyadragon]

Yep, and that's why I'd dearly love to see Bayes's Theorem as a useable tool, because it really makes us really spell out what evidence we are using and the weight assigned to it.

But I still have concerns over how to ensure that data collected can be used in BT. I've been asking for feedback from various sites, and someone sent me a scathing review of Carrier's use of BT in the Fine-Tuning Argument by Luke Barnes. I've updated my review with quotes from Barnes. Barnes also wrote about the applicability of using BT for history. From my updated review: http://members.optusnet.com.au/gakus...HJ_Review.html


That said, Barnes doesn't seem necessarily to be against BT being used for history, but rather Carrier's approach.

I do not endorse the use of BT in history, but as in other uses of BT it depends on the degree of objective basis for the criteria for determining the probabilities used in the analysis, and an objective comparison in using likelihoods and priors to calculate posteriors.

The main problem is that academic history does not try to prove nor calculate the probability of events nor the specific character of events based methods like BT.

Having a religious agenda like Craig's further hobbles the potential value of this strategy.

[One Bad Pig]

I do not endorse the use of BT in history, but as in other uses of BT it depends on the degree of objective basis for the criteria for determining the probabilities used in the analysis, and an objective comparison in using likelihoods and priors to calculate posteriors.

The main problem is that academic history does not try to prove nor calculate the probability of events nor the specific character of events based methods like BT.

Having a religious agenda like Craig's further hobbles the potential value of this strategy.

This discussion is about Carrier, not Craig. I dare say an anti-religious agenda like Carrier's is no less hobbling.

[shunyadragon]

This discussion is about Carrier, not Craig. I dare say an anti-religious agenda like Carrier's is no less hobbling.

I apologize, Carrier it is!

[GakuseiDon]

I do not endorse the use of BT in history, but as in other uses of BT it depends on the degree of objective basis for the criteria for determining the probabilities used in the analysis, and an objective comparison in using likelihoods and priors to calculate posteriors.

The main problem is that academic history does not try to prove nor calculate the probability of events nor the specific character of events based methods like BT.

I wish it did! But I think that depends on what you are examining. Peter Kirby on the Biblical Criticism & History Forum has been using BT to determine the probability of authorship of writers, by examining the frequency of words in various texts. That sounds like a reasonable approach, as it produces an objective approach.

Barnes criticism of Carrier seems to be that Carrier is a "finite frequentist", someone using the frequency of historical events to determine their likelihood. Yet historical events are nearly all "one offs". So Barnes puts his finger on the problem of using such an approach for studying history.

[shunyadragon]

I wish it did! But I think that depends on what you are examining. Peter Kirby on the Biblical Criticism & History Forum has been using BT to determine the probability of authorship of writers, by examining the frequency of words in various texts. That sounds like a reasonable approach, as it produces an objective approach.

I have no argument with this. Using it in text analysis does work as it is sometimes used today for determining authorship of many things, but that is not the issue of actually using it relating to history itself, and historical reliability of the testimony in the texts.

Barnes criticism of Carrier seems to be that Carrier is a "finite frequentist", someone using the frequency of historical events to determine their likelihood. Yet historical events are nearly all "one offs". So Barnes puts his finger on the problem of using such an approach for studying history.

I agree with this objection.

[Doug Shaver]

But I still have concerns over how to ensure that data collected can be used in BT.

I'm not sure what you mean by that. BT uses two kinds of data, background knowledge and evidence. Both are sets of facts, and they must not themselves be in dispute. If they are in dispute, then that dispute has to be resolved before a Bayesian analysis can even get started.

For example, consider Paul's reference to James as "brother of the lord." Mythicists generally don't dispute that Paul actually wrote that. But historicists will say, "Paul said James was Jesus' brother" as if it were an undisputed fact that the intended meaning of "brother of the lord" was "biological sibling of Jesus of Nazareth." That fact can be disputed and it is disputed, and it is pure question-begging to pretend otherwise. So, we have a piece of evidence, Paul's assertion that James was a "brother of the lord." Let's call it J. We'd expect Paul to say that sort of thing if Jesus actually existed, and so P(J|H) is pretty high, let's say 0.8. The historicist claim is that P(J|~H) is really low -- close to zero, to hear some tell it. The mythicist argument is that P(J|~H) is actually a lot higher than zero, probably about the same as P(J|H). And this is the argument that you will see in any debate about the implications of "brother of the lord," even if nobody participating in that debate ever says the first word about Bayes Theorem. When this particular debate arises, even if both sides will swear that Bayes Theorem is worthless as a tool of historiography, they are engaging in a Bayesian argument.

That is the sort of thing Carrier meant when he said that when history is done right, it is done with Bayes, even if the people doing it don’t know it. Now, "doing history right" does not necessarily mean, in this case, assigning a high value to P(J|~H). It means that if J is the best evidence you can offer for Jesus' historicity, then you'd better have a really good argument for claiming that it cannot have a high value. Because, if P(J|H) and P(J|~H) are about equal, then J is worthless as evidence, either for or against historicity. And if P(J|~H) is only a little lower than P(J|H), then J helps the historicist case a little bit, but not much.

I've been asking for feedback from various sites, and someone sent me a scathing review of Carrier's use of BT in the Fine-Tuning Argument by Luke Barnes.

I took a look at the Part I article that you linked to. I don't have time right now to dissect Barnes's entire commentary, but here are some preliminary observations.

Carrier's critics are justified in being put off by his style. He is cocky, condescending, and verbose. He can also be crude (by the standards of an earlier generation) when speaking before an audience. But that doesn't make him wrong.

He can also be careless. After giving a quotation from Carrier, Barnes notes, "Carrier seems to be saying that P(h|b), P(~h|b), P(e|h.b), and P(e|~h.b) are the premises from which one formally proves Bayes’ theorem." And yes, in the quoted passage, a naďve reader (which Barnes presumably is not) could get the impression that Carrier is saying that. However, anyone familiar with the actual derivation of Bayes Theorem, and with Carrier's work in general, would know good and well that Carrier could not have meant to suggest such a thing. Carrier here was guilty of sloppy writing, not, as Barnes implies, of mathematical ignorance.

What Carrier is saying is that when one uses Bayes Theorem, the four probabilities constitute the premises of an argument to which P(h|e.b) is the conclusion. This is exactly analogous to saying that if you use the quadratic equation, the constants A, B, and C constitute the premises of an argument to which the roots of the equation are the conclusion. (Also analogously, any uncertainty in those constants results in a corresponding uncertainty in the roots.) By the definition of "theorem," Bayes theorem is necessarily a true statement, which -- as Carrier keeps trying to tell people -- makes it a logically valid argument.

The actual proof of Bayes Theorem is trivially easy to find on the Internet. Understanding the proof requires familiarity only with basic algebra and basic probability theory. Those to whom either is a mystery will just have to take the experts' word for it.

A valid argument, when you have one, does not guarantee a true conclusion. What it guarantees is that if you deny the conclusion, then you must also deny at least one premise. You don't have to know which premise you're going to question, but you must insist that at least one of them is false. Otherwise, if you say, "I accept all the premises, but I can't accept the conclusion," you commit yourself to believing a contradiction.

Since we're dealing with probabilities, there is some logical wiggle room. Suppose that, on the basis of probabilities that you don't dispute, Bayes shows that the probability of a certain hypothesis is only 0.2. That doesn't mean it can't be true. You can say, "Very well, it's unlikely, but I believe it anyway." Fine. But then you can't very well say that anyone who doesn't believe it is some kind of idiot. (Whether they're entitled to think you're the idiot is beyond the scope of this conversation.)

But, about those probabilities . . . . What is probability supposed to even mean in a historical context? Barnes infers, from some material he quotes, that Carrier embraces a frequentist interpretation, which he clearly does seem to do. But in Proving History, Carrier made it clear he was talking about epistemic probability, which is a quite distinct interpretation. But epistemic probability is not unrelated to frequentist probability. For that matter, all interpretations of probability (how many there are depends on who is counting) are in some way based on or otherwise related to frequencies).

Barnes argues that under frequentism, the probability of any historical event is mathematically undefined. Every event is unique, and so there is no reference class, and so any calculation requires division by zero. And yes, a naďve application of frequentism to history would be nonsense. However, if we assume that there is such a thing as human nature, then we can recognize some patterns in how people behave. We will observe that in some situations, there are certain things people always do, and in some situations there are certain things people usually do, and certain things they rarely do, and certain things they never do.

Barnes asks: "Given the documentary and archaeological evidence, what is the probability that Caesar crossed the Rubicon in 49 BC? Well, how many times in our past experience has that evidence been associated with a known case of Caesar crossing the Rubicon?" and he answers: "None out of none. Thus, the probability that Caesar crossed the Rubicon in 49 BC is undefined." But that is a silly objection. Documentary and archeological evidence is produced by human activity, and we know, for every particular kind of evidence, what sorts of human activities usually produce it and which other sorts of human activities usually don't produce it. The documentary evidence has Caesar in Cisalpine Gaul in early January of 49 BCE, then in Italy proper by mid-January. The Rubicon River formed the border between those two places, and so if Caesar did not cross the Rubicon, then either he was never in Cisalpine Gaul or else, once there, he never returned to Italy. (Or else he took a very long detour to get back.) In either case, the documentary record is grossly inaccurate.

And of course, inaccurate documentation does happen. There is a lot of it out there. But we have some idea of the situations that cause history to be recorded inaccurately or even sometimes completely fabricated. And with that knowledge, we can make some informed estimates of the likelihood that we would have the documents we have about Caesar, and that they would say what they say about him, if he had not actually crossed the Rubicon on that particular occasion.

That said, Barnes doesn't seem necessarily to be against BT being used for history, but rather Carrier's approach.

If the question is "Can Bayes be used for history?" then Barnes does not give a clear answer. Carrier, he says, subscribes to an "outdated, overly restrictive and practically useless interpretation of probability." But Bayes' relevance to historiography has nothing to do with Carrier's particular interpretation of probability, because the mathematics is independent of the interpretation. If there is any interpretation that can be applied to historical questions, then Bayes is applicable to those questions when using that interpretation.

[shunyadragon]

I'm not sure what you mean by that. BT uses two kinds of data, background knowledge and evidence. Both are sets of facts, and they must not themselves be in dispute. If they are in dispute, then that dispute has to be resolved before a Bayesian analysis can even get started.

For example, consider Paul's reference to James as "brother of the lord." Mythicists generally don't dispute that Paul actually wrote that. But historicists will say, "Paul said James was Jesus' brother" as if it were an undisputed fact that the intended meaning of "brother of the lord" was "biological sibling of Jesus of Nazareth." That fact can be disputed and it is disputed, and it is pure question-begging to pretend otherwise. So, we have a piece of evidence, Paul's assertion that James was a "brother of the lord." Let's call it J. We'd expect Paul to say that sort of thing if Jesus actually existed, and so P(J|H) is pretty high, let's say 0.8. The historicist claim is that P(J|~H) is really low -- close to zero, to hear some tell it. The mythicist argument is that P(J|~H) is actually a lot higher than zero, probably about the same as P(J|H). And this is the argument that you will see in any debate about the implications of "brother of the lord," even if nobody participating in that debate ever says the first word about Bayes Theorem. When this particular debate arises, even if both sides will swear that Bayes Theorem is worthless as a tool of historiography, they are engaging in a Bayesian argument.

That is the sort of thing Carrier meant when he said that when history is done right, it is done with Bayes, even if the people doing it don’t know it. Now, "doing history right" does not necessarily mean, in this case, assigning a high value to P(J|~H). It means that if J is the best evidence you can offer for Jesus' historicity, then you'd better have a really good argument for claiming that it cannot have a high value. Because, if P(J|H) and P(J|~H) are about equal, then J is worthless as evidence, either for or against historicity. And if P(J|~H) is only a little lower than P(J|H), then J helps the historicist case a little bit, but not much.


I took a look at the Part I article that you linked to. I don't have time right now to dissect Barnes's entire commentary, but here are some preliminary observations.

Carrier's critics are justified in being put off by his style. He is cocky, condescending, and verbose. He can also be crude (by the standards of an earlier generation) when speaking before an audience. But that doesn't make him wrong.

He can also be careless. After giving a quotation from Carrier, Barnes notes, "Carrier seems to be saying that P(h|b), P(~h|b), P(e|h.b), and P(e|~h.b) are the premises from which one formally proves Bayes’ theorem." And yes, in the quoted passage, a naďve reader (which Barnes presumably is not) could get the impression that Carrier is saying that. However, anyone familiar with the actual derivation of Bayes Theorem, and with Carrier's work in general, would know good and well that Carrier could not have meant to suggest such a thing. Carrier here was guilty of sloppy writing, not, as Barnes implies, of mathematical ignorance.

What Carrier is saying is that when one uses Bayes Theorem, the four probabilities constitute the premises of an argument to which P(h|e.b) is the conclusion. This is exactly analogous to saying that if you use the quadratic equation, the constants A, B, and C constitute the premises of an argument to which the roots of the equation are the conclusion. (Also analogously, any uncertainty in those constants results in a corresponding uncertainty in the roots.) By the definition of "theorem," Bayes theorem is necessarily a true statement, which -- as Carrier keeps trying to tell people -- makes it a logically valid argument.

The actual proof of Bayes Theorem is trivially easy to find on the Internet. Understanding the proof requires familiarity only with basic algebra and basic probability theory. Those to whom either is a mystery will just have to take the experts' word for it.

A valid argument, when you have one, does not guarantee a true conclusion. What it guarantees is that if you deny the conclusion, then you must also deny at least one premise. You don't have to know which premise you're going to question, but you must insist that at least one of them is false. Otherwise, if you say, "I accept all the premises, but I can't accept the conclusion," you commit yourself to believing a contradiction.

Since we're dealing with probabilities, there is some logical wiggle room. Suppose that, on the basis of probabilities that you don't dispute, Bayes shows that the probability of a certain hypothesis is only 0.2. That doesn't mean it can't be true. You can say, "Very well, it's unlikely, but I believe it anyway." Fine. But then you can't very well say that anyone who doesn't believe it is some kind of idiot. (Whether they're entitled to think you're the idiot is beyond the scope of this conversation.)

But, about those probabilities . . . . What is probability supposed to even mean in a historical context? Barnes infers, from some material he quotes, that Carrier embraces a frequentist interpretation, which he clearly does seem to do. But in Proving History, Carrier made it clear he was talking about epistemic probability, which is a quite distinct interpretation. But epistemic probability is not unrelated to frequentist probability. For that matter, all interpretations of probability (how many there are depends on who is counting) are in some way based on or otherwise related to frequencies).

Barnes argues that under frequentism, the probability of any historical event is mathematically undefined. Every event is unique, and so there is no reference class, and so any calculation requires division by zero. And yes, a naďve application of frequentism to history would be nonsense. However, if we assume that there is such a thing as human nature, then we can recognize some patterns in how people behave. We will observe that in some situations, there are certain things people always do, and in some situations there are certain things people usually do, and certain things they rarely do, and certain things they never do.

Barnes asks: "Given the documentary and archaeological evidence, what is the probability that Caesar crossed the Rubicon in 49 BC? Well, how many times in our past experience has that evidence been associated with a known case of Caesar crossing the Rubicon?" and he answers: "None out of none. Thus, the probability that Caesar crossed the Rubicon in 49 BC is undefined." But that is a silly objection. Documentary and archeological evidence is produced by human activity, and we know, for every particular kind of evidence, what sorts of human activities usually produce it and which other sorts of human activities usually don't produce it. The documentary evidence has Caesar in Cisalpine Gaul in early January of 49 BCE, then in Italy proper by mid-January. The Rubicon River formed the border between those two places, and so if Caesar did not cross the Rubicon, then either he was never in Cisalpine Gaul or else, once there, he never returned to Italy. (Or else he took a very long detour to get back.) In either case, the documentary record is grossly inaccurate.

And of course, inaccurate documentation does happen. There is a lot of it out there. But we have some idea of the situations that cause history to be recorded inaccurately or even sometimes completely fabricated. And with that knowledge, we can make some informed estimates of the likelihood that we would have the documents we have about Caesar, and that they would say what they say about him, if he had not actually crossed the Rubicon on that particular occasion.


If the question is "Can Bayes be used for history?" then Barnes does not give a clear answer. Carrier, he says, subscribes to an "outdated, overly restrictive and practically useless interpretation of probability." But Bayes' relevance to historiography has nothing to do with Carrier's particular interpretation of probability, because the mathematics is independent of the interpretation. If there is any interpretation that can be applied to historical questions, then Bayes is applicable to those questions when using that interpretation.

Excellent commentary! Learned some stuff.

[Doug Shaver]

Thanks, Shuny.

[GakuseiDon]

Yes, I agree with Shunyadragon. Thanks Doug, that was most useful. I'm still mulling over the implications. I certainly agree with Carrier that many people argue using a Bayes-type approach informally, even in history, as you also point out above. But my concerns are about the facts being entered into the Theorem, rather than the Theorem itself. I'm thinking over your example of using 'brother of the Lord', and how we would get to apply a value for it even for H, something I may come back to.

On the 'brother of the Lord', Carrier writes on page 592:

In other words, I actually think this evidence is twice as likely on mythicism, but, though I doubt it, I'll allow that it might be twice as likely on historicity. I certainly cannot reasonably believe these passages (including their internal ambiguity and surrounding silence) are any more expected than that on h than on (not)h.

Things like that raise red flags. I understand that a subjective approach is required, but IMHO this reversal is just too subjective. After 10 pages of building his case, he reverses his input figures right at the end. I understand that he is arguing a fortiori at the end, but there is little to no justification for the reversal that I can see. And there are many similar examples. If some inputs can be so uncertain, it makes me wonder if they can be used at all.

Anyway, thanks for your comments on this. I think I need to understand the practical aspects of using Bayes's Theorem to do a decent critique on Carrier's use there, but I lack the time to study the subject in such detail. :(

[Doug Shaver]

You're very welcome, Don. I've been working on some followup comments, but I'm not satisfied yet that they add any of substance to what I've already said. I'll work on them some more and see what happens.

[Doug Shaver]

Things like that raise red flags. I understand that a subjective approach is required, but IMHO this reversal is just too subjective. After 10 pages of building his case, he reverses his input figures right at the end. I understand that he is arguing a fortiori at the end, but there is little to no justification for the reversal that I can see. And there are many similar examples. If some inputs can be so uncertain, it makes me wonder if they can be used at all.

He explains how the figures are useful notwithstanding the uncertainty.

Our uncertainty is rarely total. We usually have some defensible range of probabilities: not less than x, not more than y. And Carrier explains the usefulness of probabilities even with wide ranges: they give us a defensible range of consequent probabilities. Suppose you plug in the estimate that are most favorable to the hypothesis, and you get a consequent probability of 0.7. Then you do the calculation again and you use the estimates least favorable to the hypothesis, and your consequent is 0.3. In that case, you now know something that you did not know before about your hypothesis: You know how inconclusive the evidence for that hypothesis is. That is, unless you are committed to a set of estimates that result in a particular consequent probability. But even in that case, you now know where you need to focus your arguments. You need to defend the probabilities that gave you that consequent.

But my concerns are about the facts being entered into the Theorem, rather than the Theorem itself. I'm thinking over your example of using 'brother of the Lord', and how we would get to apply a value for it even for H, something I may come back to.

I don't know an algorithm for figuring those probabilities, but that doesn't mean everyone's guess is as good as anyone else's. The first thing that has to happen is for the parties to the dispute to stop insulting each other and present some arguments that reasonable people can discuss in good faith.

Bayes isn't going to tell us right away whether Jesus really existed, and I don't recall Carrier ever suggesting that it would. It isn't supposed to end the debate. It's supposed to get a productive debate started. Bayes ought to get the parties to the debate to begin focusing their attention on the real evidential issues about which they have honest disagreements and then identify the bases of those disagreements. If historicists actually believe that the probability is near zero that Paul's "brother of the lord" meant something other than "sibling of Jesus," then they need an argument defending that belief. If they don't have one, then mythicists don't even need a counterargument. Whatever historicists can assert without argument, mythicists can deny without argument.