Bayesian Probability... in Space! (uhm... History)

[Peter Kirby]

Yesterday I attended a talk by Richard Carrier at UCI and went to the pub with him and others afterward. This specific talk was mostly about Bayes and had very little to say, directly, about the historicity of Jesus. Since it seems to be of interest to people here, and in appreciation of the talk I heard, I picked up a copy of Proving History too. This post will make some general comments that are my own. The next post will be working out of my notes from the talk. Perhaps at a future date I can comment on the book, after I've read it.

Reviews of Carrier's books form a very "biased sample" of opinion on the application of mathematics to real-world problems. If it's not completely clear what I mean already, then it's simply this: reviews of Carrier's books are reacting specifically to Carrier's actual central hypothesis (re: "MinMyth" vis-a-vis "MinHist" and "why we might have reason for doubt") and reacting generally to Carrier's specific application of Bayes' theorem in this context (i.e., the resolution of the question of the historicity of Jesus). Besides the facts that the reviewers can be influenced by human subjectivity (one meaning of the word "biased"), the sample itself is "biased" because it is a very non-random selection out of the total pool of opinion on the application of mathematics to real-world problems.

While I appreciate the search for at least one reviewer with credentials in mathematics who can "back him up" (and I've conducted no search at all, personally--though I vaguely recall that Carrier himself submitted his manuscripts to one or more persons prior to publication for exactly that kind of review [unfortunately, my memory does not come with page numbers]), the general argument can't really be settled by such polling. All we really know from the fact of this argument is that the argument is real and worthy of our attention.

With this in mind, I don't really see the point of referring the general question back to Carrier all the time (that's why the first quote has an ellipsis), as if he's the first to try anything like this. (No, he's not the first to try anything like this.)

from that other thread: http://www.earlywritings.com/forum/view ... f=3&t=1317

I don't see a problem with ... providing best/worst case odds myself. IMHO ... approach is reasonable, and says more about the subjective nature of the evidence ...

I wouldn't call the odds 'suspicious' but rather 'subjective'.

Given the subjective nature of the evidence available, I suspect that each person will end up with their own odds, which is a problem in itself.

suspect, due to his insistence on applying subjective quanities to an objective theorem

When we’re dealing with rare evidence for rare events, then small errors in the inputs can end up giving a huge range of outputs, enough of a range that there is no usable information to be had... These issues combine to make it very difficult to make any sensible conclusions from Bayes’s Theorem in areas where probabilities are small, data is low quality, possible reference classes abound, and statements are vague.

If the author is correct, it sounds like BT is simply not suitable when the probabilities are based on guesses.

for investigating history, where the data is of low quality, etc. It becomes "Garbage In, Garbage Out."

The problem is about the Bayesian theorem not applying to cases where the inputs are highly suggestive & can very greatly differ from one person to another.

This is all well and good, as one option for an opinion, and I'm sure there are some mathematicians that would stand for all of the above.

If I understand correctly (and this is me speaking--I haven't read Proving History yet), some of them would self-identify as frequentists. To reduce a complicated subject to the bare basics (possibly misrepresenting it along the way), frequentists believe in the real objectivity of probabilistic statements. Not in the sense of the "completely neutral observer, with limited information" (which would be one of two interpretations of Bayesian probability--the other is "subjectively interpreting observer, with limited information," and that seems to be the sense in which someone Proving History would use her or his probabilities when it is necessary to do so) but in the sense of "God himself looking down" (which is frequentist probability).

So, for a hypothesis, which is either true or false in objective reality ("God himself looking down"), the strict frequentist says that it's probability is either 0 or 1, corresponding to false or true. After all, he's counted (or the Universe has counted, if he can't), and there's only one value to count.

Bayesians interprets the "probability" of a hypothesis that is either true or false differently than a frequentist. It assigns it a range from 0 to 1, and it does so with reference to the limited information that the observer has relevant to the hypothesis. Now, mathematically, this is not a contradiction, because they're describing different things. What they really disagree over is what the most useful definition of "probability of a hypothesis" is. (Or, sometimes, perhaps they both think that the Bayesian definition could be useful, but the frequentist might still think that to attempt to work with it mathematically is bollocks, for whatever reason. Either way, Carrier didn't create this controversy. It is centuries old, with the frequentist interpretation seeming to have the limelight in the mid-20th century but seemingly having less importance before or after.)

The most relevant wiki page (and I should have linked it earlier) seems to be:

Bayesian probability

And here we find this very debate, being played out in a completely general sort of way:

Broadly speaking, there are two views on Bayesian probability that interpret the probability concept in different ways. According to the objectivist view, the rules of Bayesian statistics can be justified by requirements of rationality and consistency and interpreted as an extension of logic. According to the subjectivist view, probability quantifies a "personal belief".

Broadly speaking, there are two views on Bayesian probability that interpret the 'probability' concept in different ways. For objectivists, probability objectively measures the plausibility of propositions, i.e. the probability of a proposition corresponds to a reasonable belief everyone (even a "robot") sharing the same knowledge should share in accordance with the rules of Bayesian statistics, which can be justified by requirements of rationality and consistency. For subjectivists, probability corresponds to a 'personal belief'. For subjectivists, rationality and coherence constrain the probabilities a subject may have, but allow for substantial variation within those constraints. The objective and subjective variants of Bayesian probability differ mainly in their interpretation and construction of the prior probability.

The page continues with some remarks on "Personal probabilities and objective methods for constructing priors":

Following the work on expected utility theory of Ramsey and von Neumann, decision-theorists have accounted for rational behavior using a probability distribution for the agent. Johann Pfanzagl completed the Theory of Games and Economic Behavior by providing an axiomatization of subjective probability and utility, a task left uncompleted by von Neumann and Oskar Morgenstern: their original theory supposed that all the agents had the same probability distribution, as a convenience.[21] Pfanzagl's axiomatization was endorsed by Oskar Morgenstern: "Von Neumann and I have anticipated" the question whether probabilities "might, perhaps more typically, be subjective and have stated specifically that in the latter case axioms could be found from which could derive the desired numerical utility together with a number for the probabilities (cf. p. 19 of The Theory of Games and Economic Behavior). We did not carry this out; it was demonstrated by Pfanzagl ... with all the necessary rigor".[22]
Ramsey and Savage noted that the individual agent's probability distribution could be objectively studied in experiments. The role of judgment and disagreement in science has been recognized since Aristotle and even more clearly with Francis Bacon. The objectivity of science lies not in the psychology of individual scientists, but in the process of science and especially in statistical methods, as noted by C. S. Peirce.[23] Recall that the objective methods for falsifying propositions about personal probabilities have been used for a half century, as noted previously. Procedures for testing hypotheses about probabilities (using finite samples) are due to Ramsey (1931) and de Finetti (1931, 1937, 1964, 1970). Both Bruno de Finetti and Frank P. Ramsey acknowledge[citation needed] their debts to pragmatic philosophy, particularly (for Ramsey) to Charles S. Peirce.
The "Ramsey test" for evaluating probability distributions is implementable in theory, and has kept experimental psychologists occupied for a half century.[24] This work demonstrates that Bayesian-probability propositions can be falsified, and so meet an empirical criterion of Charles S. Peirce, whose work inspired Ramsey. (This falsifiability-criterion was popularized by Karl Popper.[25][26])
Modern work on the experimental evaluation of personal probabilities uses the randomization, blinding, and Boolean-decision procedures of the Peirce-Jastrow experiment.[27] Since individuals act according to different probability judgments, these agents' probabilities are "personal" (but amenable to objective study).
Personal probabilities are problematic for science and for some applications where decision-makers lack the knowledge or time to specify an informed probability-distribution (on which they are prepared to act). To meet the needs of science and of human limitations, Bayesian statisticians have developed "objective" methods for specifying prior probabilities.
Indeed, some Bayesians have argued the prior state of knowledge defines the (unique) prior probability-distribution for "regular" statistical problems; cf. well-posed problems. Finding the right method for constructing such "objective" priors (for appropriate classes of regular problems) has been the quest of statistical theorists from Laplace to John Maynard Keynes, Harold Jeffreys, and Edwin Thompson Jaynes: These theorists and their successors have suggested several methods for constructing "objective" priors:
Maximum entropy
Transformation group analysis
Reference analysis
Each of these methods contributes useful priors for "regular" one-parameter problems, and each prior can handle some challenging statistical models (with "irregularity" or several parameters). Each of these methods has been useful in Bayesian practice. Indeed, methods for constructing "objective" (alternatively, "default" or "ignorance") priors have been developed by avowed subjective (or "personal") Bayesians like James Berger (Duke University) and José-Miguel Bernardo (Universitat de València), simply because such priors are needed for Bayesian practice, particularly in science.[28] The quest for "the universal method for constructing priors" continues to attract statistical theorists.[28]
Thus, the Bayesian statistician needs either to use informed priors (using relevant expertise or previous data) or to choose among the competing methods for constructing "objective" priors.

Accordingly, we must make an important distinction. The use of Bayes' theorem against "subjective" probabilities is controversial within mathematics (and in the sciences) but is not controverted by mathematics. Not all mathematicians would want to use Bayes' theorem with "subjective" probabilities, but mathematics itself doesn't tell us whether we should or should not do so. Mathematics simply tells us how to do so, if we really want to go down that road.

This is basically a form of the old "is-ought" problem, except that what might be true of philosophy in general is certainly true for math. Math can't tell you whether you "ought" to do something. For example, it can't tell you whether you should attempt to express your subjective opinions in probabilistic form. What it can do is tell you how to work with these numbers after you have them, which is what it does in the form of Bayes' theorem and the method of updating prior probabilities with the consequent probabilities in order to calculate posterior probabilities. The first part, choosing to express opinions as probabilities, is just as human and subjective a decision as the numbers representing the guesses; the second part is just the math.

I would just make a couple final comments, however. Keep in mind what we are calling "Garbage" here, in the phrase "Garbage In Garbage Out." If what we are calling "Garbage" is just one person's particular opinions, then that's not a problem whatsoever, Bayes or no Bayes--just ignore them and use the non-garbage instead. But I do get the feeling that people mean more than just one person's wayward beliefs and that this "Garbage" is seen as a real problem for us all, not just as an individual's problem. GakuseiDon (and the author he summarizes here) said it this way: "for investigating history, where the data is of low quality," GIGO. What we are calling "Garbage" in this phrase is the state of our knowledge of the facts. If that is "Garbage," it is a problem for everybody. Avoiding precise mathematical representation doesn't help us out of the swamp. Maybe it makes us feel better about being in a swamp of "garbage" opinions, but "Garbage In Garbage Out" is true even if you are just "muddling through" this swamp.

Just letting loose a little with another comment (and this is still just me talking). And in what way are we enlisting math in this swamp, if we do at all? I'm going to have time to talk about this a little more, when summarizing Carrier, but here's just a single paragraph. Before I've called it an "aid to honesty." Another way of putting that phrase is "an accountability measure." Basically it's just bookkeeping. It's keeping track of what the assumptions are and what weights have been assigned for these assumptions. It's formal logic with some numbers, because history deals in uncertainty and not with certainty. And it's better than the deductive method in this application for various, formal reasons (mostly because deductive reasoning is terrible at bookkeeping, works best only if everything is 100% full-steam-ahead True, and is especially terrible at representing results as anything other than a simple binary true or false). Who has a problem with bookkeeping? Mostly people that don't like keeping books. Which is most people. I know I wait to do my taxes until April. It's cumbersome and difficult for most, and it's just cumbersome for the rest. The only reason we'd ever use it in history, really, is when the matter is very controversial and somewhat ambiguous. The controversy makes the bookkeeping more help than hurt (because everything is challenged at some point), and the ambiguity makes the exercise more than pure wank (like trying to prove that the world didn't pop into existence last Tuesday). Now that doesn't mean we have to do so. But it might mean that we can without looking too foolish.

[Peter Kirby]

These are excerpts from my notes, written in narrative form. Unless in quotation marks, it is not verbatim. If it's in parentheses, it's not from him at all. In general, this is an elaboration of my notes and may or may not be an exact representation of what was said.

Carrier starts out talking a little bit about why he came to write these two books at all, Proving History and On the Historicity of Jesus. The first thing he mentions in this regard is that he received his Ph.D. in Ancient History from Columbia University in 2008. There were no jobs opening up for humanities professors at that time, and in fact universities were cutting back on the number of positions. That's when he was approached by fans with the idea of a "grant" that would allow him to take the time to write on one particular historical subject. Because he was entrusted with this "grant" by other people to do a good job, he took his work very seriously as a result. Carrier also mentions that he had complete academic freedom to form any conclusion, and likewise that the sponsors had every right to disavow his work.

His first job was to work on methodology, a subject covered in the first book, Proving History. And the first job there was to look at what method has been used up to now. And he was thus struck by something. Not only was the methodology regarding the Historical Jesus used up to now really bad. But when he reviewed the literature, everyone who subjected this methodology to a very detailed and precise examination recognized that very thing: the methodology being used was really bad. Therefore, and because of this, Carrier took his first task as devising a new methodology in the study of the subject of the Historical Jesus.

Then Carrier mentions that his book (On the Historicity of Jesus) is so large because peer review required him to answer many objections. Whenever an academic peer who was looking over the work came up with any kind of objection, Carrier was obliged to put that objection into the book and come up with a response to it. Carrier then briefly mentioned that his book is starting to get some academic attention, partly due to his talk at the Pacific conference hosted by the SBL in Azusa on the Monday two days prior.

Back to the problem of methodology, Carrier mentions that everyone was using the same flawed methodology and getting different results. Clearly, he says, that indicates some kind of problem. (How do scholars resolve these differences among themselves? Does their methodology even support such an attempt?)

So Carrier then goes over basic humanities research principles. What he finds would shape the structure of his entire argument. What he finds is that Bayesian reasoning is hidden in the structure of existing historical arguments, generally. It's already implicit. To make it explicit, all he needed to add was "6th grade math."

Carrier tucks away all the really hard math (which isn't necessary in order simply to use Bayes' theorem) in the back of the Proving History volume.

In On the Historicity of Jesus, Carrier starts by going over the problem and then carefully defining the rival hypotheses. Chapter 2 defines minimal historicity, and chapter 3 defines minimal mythicism. Then chapters 4 and 5 go over the background knowledge for the subject.

Lots of the context that Carrier describes in his book is generally understood, but rarely is it presented all together by one person (or present in one person's reservoir of information). Therefore he goes over all of it (in a way that benefits both the general reader and the specialist).

Chapter 6 discusses priors. Chapter 7 goes over the problems of the evidence. Chapters 8, 9, 10, and 11 go over four different major categories of evidence (Acts, Gospels, Epistles, Extrabiblical).

Carrier mentions here that he designed his book in such a way that you can go through and put in your own numbers. You don't have to trust his particular judgment.

Carrier then goes on to quote scholars showing some of the chaos in the existing quest for the historical Jesus with the existing methodology, such as it is. (I did not take down any of the quotes, but I assume they're found in Proving History or on his blog or something.)

Then come two of his most central claims:

• "All historical argument is probabilistic (all premises consist of statements of probability, overt or covert)."
• "Hypotheses in history assert what most likely happened in the past." Therefore it is math.

And a third:

• Bayes' Theorem is a model applicable to every instance of empirical reasoning, whether you are aware of it or not and whether you use it or not.

Carrier has aimed his books to the humanities scholars (not mathematicians, statisticians, or scientists) and used 6th grade math (with, of course, the non-6th grade element of the Bayes' theorem equation itself). He wants everyone to be comfortable with formalizing empirical arguments in terms of math. He maintains that this allows us a more precise understanding of how we are actually arguing.

Further, because we are already implicitly using Bayes' theorem, explicitly using it lets us be more clear about which exact numbers we are arguing about. There are three numbers of concern here.

(1) Relative prior probability (alternatively, the prior probability of the positive hypothesis h; this is a single number to argue over, because knowing any such value--the prior probability of h, the prior probability of ~h, or the ratio of these two--lets you compute all the others).

(2) The probability of P( e | h ) -- the conditional probability of the evidence e, given the hypothesis h.

(3) The probability of P( e | ~h ) -- the conditional probability of the evidence e, given the hypothesis ~h.

He contends that every informal argument you've ever had about empirical subjects--every single one--could be represented in this form.

Then he gives a specific example of the claim found in Mark 15:33 and parallels, that the Sun went out for a full three hours during the crucifixion.

First, how typically does the sun actually go out? (relative prior probability)

Second, how likely is the evidence we have if the hypothesis is true and that happened?

Third, how likely is the evidence we have if the hypothesis is not true and it didn't happen? I.e., basically, how typically are such miracle claims just made up?

If you did this math, you'd find out that the probability that the sun went out for three hours is very small. You are doing this kind of reasoning in your head, even if you didn't formulate it in mathematical terms.

(1) All historical reasoning is probabilistic, and all probabilistic reasoning is mathematical.
(2) Imprecision and uncertainty can be modeled mathematically.

Carrier says that most people and most professionals are with him up to this point, but they have a problem here:

(3) "Math is too hard." (not his opinion, but that of those who don't want to use math in history)

At this point Carrier specifically recommends Danica McKellar's book "Math Doesn't Suck." It covers junior high math, which is all you need to understand the math used in his book.

Now Carrier goes on to talk about some of the informal principles of reasoning that are all contained and concealed, without any fiddling, in the simple mathematical expressions that go into Bayesian reasoning.

First, there are some common mistakes that people recommend avoiding, all of which are avoided by using Bayesian reasoning. And a lot of these mistakes are frequent problems in the secondary literature in history.

(1) Possibly, therefore probably
(2) That which explains the evidence is therefore true
(3) Unlikely things don't happen [period]
(4) Argumentum ad hoc

In this last one, it means that arguing for a hypothesis by inventing excuses for it to seem better is fallacious.

All of these principles can and are expressed with probability theory. But the mathematical formulation doesn't just help us avoid informal fallacies; it also helps us understand how to reason, in a positive way, as expressed in several aphorisms.

(1) "Extraordinary Claims Require Extraordinary Evidence"
(2) "Absence of Evidence Sometimes Is Evidence Of Absence"
(3) "Ockham's Razor Does Cut"

(Because the probability of each added assumption must then be multiplied in when it's conjoined to the hypothesis, thus lowering the hypothesis' prior probability even as it may improve a particular consequent probability.)

Bayes' Theorem does not just provide a framework that allows us to reason in accordance with these aphorisms that help us avoid bad reasoning and seek out good reasoning, although it does that and does that robustly. It also is contained in all of the five types of evidence that scholars in the humanities use.

Good Evidence (vs Bad) -- 5 types

(1) Physical-Historical Necessity. E.g., Caesar crossing the Rubicon.
(2) Physical Evidence (directly, e.g. coins, etc.).
(3) Unbiased Or Counterbiased Sources
(4) A credible critical account
(5) Eyewitness account

What all of these five admissible types of evidence have in common is that they are unlikely if the hypothesis were false (but perfectly likely if it is true). Thus, historians are already thinking like Bayesians (whether they realize it or not).

(But Wait, There's More! Bayes' Theorem also drops in and replaces the 'argument to the best explanation' type of expression of historical reasoning.)

Argument to the Best Explanation

(1) Explanatory Fitness
(2) Plausibility
(3) Explanatory Scope
(4) Ad Hoc-ness
(5) Explanatory Power

(So why is it better?) Once you take these criteria and express them in probabilistic form, which indeed they already are (just without numbers attached), then you can quantify the comparison of several hypotheses. You elucidate the last step (which is otherwise left opaque) of how you actually go from applying these criteria to selecting one single hypothesis (and not the others) as the 'best' explanation.

(Then Carrier goes on to explain why principles like these, which are encapsulated in Bayes, are better than the methodological ideas found in HJ studies.)

The Criterion of Embarrassment (Is it any good?)

(No.)

(1) The earliest gospel is already 40-50 years later than the time of Jesus, roughly the span of an entire human lifetime back then. Embarrassing material (if truly embarrassing) would already be suppressed by then in the retelling.

(2) We don't really know what's embarrassing (not omniscient in that regard).

(3) Any reason at all to include the story (and there must be some kind of reason to include the story) must also be a reason to invent it (e.g., Attis' castration might be abstractly embarrassing, presumably, but had a reason for its invention)

(4) If everyone is saying it, in what sense were they embarrassed by it anyway? (e.g., the crucifixion)

John's Baptism (Is it a great example of it at work?)

(No.)

(A) It sets up Christ as the model for Christian baptism.

(B) It sets up Jesus for the sinless state desirable for his adoption by God.

(C) John's reputation is coopted (even in the earliest account he endorses Jesus)

(And this baptism hypothesis can indeed by evaluated in a Bayesian fashion, etc...)

These kinds of considerations apply across the board: the crucifixion, Nazareth, Judas, being disbelieved in his hometown. (None of it is really "embarrassing" in the sense that it must be historical therefore.)

[[Digression alert---this is not really the subject of this thread.]]

The Ascension of Isaiah (and now we come to the bit that's more about the book OHJ)

It seems to be from 80s to 130s AD in its earliest identifiable recension (parts of it are later, and parts of it might be earlier).

• Prophet Isaiah is receiving a vision.
• The earliest redaction lacks visit to earth.
• This gospel is closer in belief to 1 Cor 2 and Phil 2 than NT

Philo of Alexandria actually attests to a pre-Christian Jewish belief in a celestial being named 'Jesus' (like Rom 8:29, 2 Cor 4:4, 1 Cor 8:6, and Hb 2:17, 4:14 in some of the statements).

Christians took this Jewish myth and assigned his death and resurrection to somewhere in "outer space" (lower heavens... I guess this is the vernacular according to Carrier). Even Adam was considered to be buried in "outer space" (lower heavens), somewhere around Venus/Mars (as far as the numbering of the heavens, depending on how you match up the correspondences [i.e., the third heaven... why is this so hard to say]).

Lots of cultures were assimilating their beliefs to the ideas of a dying-and-rising savior figure.

Some such figures were Osiris, Adonis, Romulus, Zalmoxis, Innana. Innana had a temple in Tyre.

• They are all "saviors".
• All go through "passion."
• All obtain victory over death.
• They all have stories that were set on earth.
• None of them were historical persons.

The epistles (50s AD) speak of a pre-existent celestial being and a revealed gospel.

Gospels (70-130 AD) are wildly fictional. No other evidence from the first half century of Christianity can extricate us from that fictionality.

The Josephus and Tacitus passages, as argued in his essays, are interpolated.

Indeed forgery may be considered to be the most typical mode of composition/authorship in the early stage of the church. (Not unlike that of the intertestamental period which we call the time of the "pseudepigrapha"?)

2 Peter 1:16 ... this is a forgery... it is answering otherwise-unknown Christians claiming that Jesus was a cleverly-designed myth (offering one of a few possible clues to such an idea that have survived). Also, Irenaeus mentions those taking the gospels as cosmic allegories.

Carrier quickly wraps it up by saying that in his book, when he did his math (with the most generous figures that he could assign in good conscience), he came up with the figure of a 1/3 likelihood (posterior probability) of the historicity of Jesus.

[[Digression alert over---although I guess a thread might always wander and I can always just split off a tangent that arises.]]

Then he mentions a bit from the SBL on Monday, where a scholar had advanced the hypothesis that Acts might have omitted the outcome of Paul's trial in a form of imitation of Pliny's letter on the status of Christians where he does not mention the outcome himself.

I ask a question. I say that Carrier did a good job in the second volume of presenting the issues, but I wonder whether Carrier believes that he may have tainted the thesis of the first book, leading scholars to reflexively reject it, because of its association with the second.

Carrier says in reply that the only objection that tends to come up in the discussion of Proving History is just that historians don't like math. Carrier goes on to mention some usage (flip-flopping) of Bayes' theorem by Christian apologists (Craig, etc.). At first they wanted to use Bayesian reasoning, when they thought they could press it into service for apologetics. Then they found out (or their critics replied) that it doesn't work that way and indeed tends to undermine Christian beliefs (when considered in fairness, in Bayesian terms). So they flipped to being anti-Bayes. But in general he finds that the apologists (unlike the historians) don't like it because it doesn't support their conclusions (while the historians don't like it because they don't like math).

Someone asks whether Carrier had ever bothered to try applying Bayes' theorem to the Roman myths.

Carrier says no, mostly because it is too obvious. The numbers are too small to labor over it much. But, we could. We could work out that Socrates existed, for example, if we wanted to, using Bayesian reasoning. And the result would be a lot higher than it would be in the case of Jesus. Carrier further says that it's especially important to bring up Bayes explicitly in ambiguous cases, to make your assumptions and/or biases more clear. This is because all historical argument is subjective and ambiguous; that's just how it is.

Carrier then mentions that the the person who had spoken for the other side at the SBL on Monday (a minister) had an anti-Bayesian argument, of sorts: One, The math was too hard for him to understand. But, Two, Isn't it convenient that the math supports Carrier's answer? Most of what his opponent had to say did not have too much to do with the structure of his argument and focused more specifically on questions of interpretation. Carrier said that he'd attempt a write-up of Monday's debate later. At this point, however, Carrier mentions that the audience seemed to understand that the speaker wasn't being completely fair in his analysis. They had some pointed questions for the other speaker, while Carrier had actually expected a lot more of the heat to be on him.

Carrier further mentions that he would likely not have covered this subject at all if it had not been chosen as the subject for his contract. He says that he was very much "adamantly against mythicism." He was pro-historicity. He thought that the mythicist writers were just cranks and that their ideas were ridiculous. But a bunch of people, whose opinions he respected, bothered him to read Doherty's book, The Jesus Puzzle. And, he says, he was kind of bothered by how good it was. At that point he became an agnostic on the question.

Carrier says that, in general, a lot of the response he gets professionally is intrigue. While there are some few secular scholars who seem to be deeply invested in some particular hypotheses, he says that most of the opposition seems to come from apologists. He says something about at least 7 scholars being on record as being, at least, agnostic, and more not being on record. But, he says, time will tell how this idea is ultimately received.

Carrier mentions Hitler, Homer, Bible, Christ (a play on Tinker, Tailor, Soldier, Spy) as a collection of various essays he's written.

Carrier says that what he enjoys (most), when discussing (historical) apologetics, is all the interesting history that comes up in the explanation of matters.

There end my notes for the talk and the questions afterwards.

One of my questions at the pub regarded what future publications we might hope to see from Carrier on historical topics. There were several competing projects that Carrier wanted to work on, including several philosophical projects, with the first mentioned related to his Sense and Goodness WIthout God. But there were some historical topics that seemed to be on the back burner. First of these would be a book summarizing his dissertation on ancient science. Then, it is not so clear, but there is the possibility that he might want to visit the general topics of mystery religions and/or savior figures in the ancient Mediterranean. I say that this is an excellent idea and would fill a real gap.

[Peter Kirby]

One thing that you really came away from the talk realizing is how very important Bayes' Theorem is to everything Carrier is doing in terms of contentious historical propositions. This isn't just "a Jesus thing" (everyone knows we've had enough of methods that only are applied in the case of Jesus!). It's fundamental to his philosophy of history, and he's given it quite some thought. And that's why we find it outside of these books too (for example, in his essay on whether there was an interpolation into Tacitus at Annals 15.44--even though the editor of the journal seems to have demanded that Carrier cut out most of his material relating to Bayesian methods).

His popular presentation for the historicity of Jesus, specifically, is clearly deficient. There are huge gaps here in the talk. But that's to be expected. He had two hours to go over almost 1000 pages of material found in his work, which itself summarizes a huge topic. There's just enough meat on the bones here to whet the appetite; those who want to dig in will have to buy the books.

Carrier's decision to focus on the Bayesian reasoning part seems to be well-received. I am a bit surprised to find that the first book, Proving History, sells out. The audience is primarily of skeptical bent (with some exceptions) and apparently appreciates the general focus on method.

While the presentation specifically of the historical evidence regarding the historicity of Jesus can't be considered anything more than a teaser, the presentation on Bayes' theorem and its application to history is much more than that. Here is the real subject of the lecture. Carrier goes through many of the key strengths of using Bayesian reasoning, and perhaps his strongest point is that you are using it already. This point is made in two ways:

(1) You're using probability when expressing your maybes/likelies/etc. Probability is math, and math is amenable to mathematics, including Bayes.
(2) You're using the comparison of the ratio of consequent probabilities and prior probabilities, implicitly, when doing historical reasoning. But instead of using a mashup of aphorisms and a list of historicity-virtues without any way to apply them, the Bayesian method spells things out clearly and succinctly.

These two points, the heart of the talk, were made quite well. With all the caveats caveated, and with all the objections defused, there doesn't seem to be anything wrong, to me, for either of these two arguments ... so long as they are understood only to underscore the fact that Carrier is not doing anything fundamentally very different to sound historical reasoning (when it isn't using Bayes explicitly) when he is using Bayes' theorem, explicitly.

They don't completely rule out contentions that, yes, Carrier might be going about things in a reasonable way, but, hey, I don't want to. And Carrier seems to realize this, at the end of the day, when mentioning that the first and foremost objection is that historians say they don't want to use math, generally.

And those objections can be made. Historians have been hobbling along just fine with their best explanations and their aphorisms to live by. Who is Carrier to tell them that suddenly historians all need to go back and learn 6th grade math all over again?

But, Carrier might say, gains are to be had! The precision is worth it. The assumptions are thus laid bare.

What precision? As everyone has by now commented, there is a huge range of subjective probabilities that can be assigned, and even on his own account the difference between the "a forteriori" results (what he considers reasonable, but hedging as much as possible pro-historicity) and his own well-considered estimates result in vastly different posterior probabilities.

All it takes is someone with slightly more hedging for historicity (and it doesn't take much, just a whiff), and the "a forteriori" result would be bumped over 50% chance of the historicity of Jesus. In the public perception, that's a significant difference (...although, to be fair, a statistician might observe that the fundamental observation expressed by 1/3 and 1/2 or even 2/3 is in each case, actually, grave uncertainty, to the point of being practically unusable as a conclusion).

And does it really take Bayes to lay all the assumptions bare? I am pretty sure that I did this without Bayes in my own essay, "The Historicity of the Empty Tomb Evaluated" (taking a cue from Benjamin Franklin). And I even used numbers (on a scale of 1 to 5, for each reason, for each side, respectively). That laid assumptions fairly bare. And all that was required for a final comparison was arithmetic (addition).

You might say that you need Bayes to convert all that into final probabilities. But are the final probabilities all that meaningful? Here we come back to the question of false precision, or the appearance of false precision. One of my critics drastically revised my numbers and came out with drastically different sums on each side. It would be a bit silly for us to be using figures such as "It's 80% shown to be nonhistorical" and "It's 98% shown to be historical," even if that's exactly what our summation seemed to add up to. Our own subjective inputs didn't have anything near that kind of precision.

More importantly, and statistically speaking, the more such imprecise figures you mash together (to compute a figure that depends on the accuracy of all previous figures), the more imprecise the results become (greater 'variance', measuring the dispersion).

Perhaps the best that could be said in each case is whether we were for or against or neither; and if so, whether we were uncertain or certain. But this is the language that is used all the time in historical literature already. How useful is it to distinguish between the various grades of probability with numbers, when those numbers are based on nothing more than hunches, and our hunches themselves do not carry much precision alone, let alone mashed all together?

Finally, while it is true that the Bayesian form lets us do everything we could want to do, formally, for the most part, is it true that we'd need it in order to formalize? Perhaps not. It is conceivable that we could formalize using deductive reasoning if we added a modal component, specifically to distinguish between the various categories: positive+certain, positive+uncertain, neutral, negative+certain, and negative+uncertain. It could be done, perhaps.

Another possible problem with subjective probabilities in explicit Bayesian methods, given that the degree of subjectivity allowed in the inputs generally means that the individual investigator might be suspected of arranging his outputs to fit. Then again, the same could be said of arguing without Bayes.

Now actually I don't think that any of these objections are insuperable, but I did want to write a few down that came to mind, in all fairness.

[Peter Kirby]

And that's all I have to say about that... for now.

[GakuseiDon]

Nice summary, Peter! Looking forward to the rest.

I would just make a couple final comments, however. Keep in mind what we are calling "Garbage" here, in the phrase "Garbage In Garbage Out." If what we are calling "Garbage" is just one person's particular opinions, then that's not a problem whatsoever, Bayes or no Bayes--just ignore them and use the non-garbage instead. But I do get the feeling that people mean more than just one person's wayward beliefs and that this "Garbage" is seen as a real problem for us all, not just as an individual's problem. GakuseiDon (and the author he summarizes here) said it this way: "for investigating history, where the data is of low quality," GIGO. What we are calling "Garbage" in this phrase is the state of our knowledge of the facts. If that is "Garbage," it is a problem for everybody. Avoiding precise mathematical representation doesn't help us out of the swamp. Maybe it makes us feel better about being in a swamp of "garbage" opinions, but "Garbage In Garbage Out" is true even if you are just "muddling through" this swamp.

I think that this is a very, very important point, and the problem that I see for the historicist side. If the data is so poor, and the evaluations are so subjective, then how can we can conclude in favour of historicity in the first place? But if the data is enough to come to some kind of objective decision on elements, then why not plug them into Bayes Theorem? It seems that these are contradictory premises. Either the data is good enough to come to a decision or it isn't.

Something I'm still mulling over!

[maryhelena]

The Mythical Jesus - An SBL Regional Report

http://simonjjoseph.blogspot.co.uk/2015 ... eport.html

• ''Carrier was clearly aware that he was not preaching to the choir. He summarized his central thesis - that Jesus originated as a celestial myth about a crucified dying-and-rising savior god. According to Carrier, "Jesus" never existed except as an imaginary celestial being who telepathically communicated and appeared to hallucinating “disciples.” The figure of “Jesus” was then historicized via a process known as “Euhemerization.” Carrier assumes a formidable burden of proof in arguing against the consensus of scholarship on multiple fronts. He dismisses Josephus’ references to Jesus. He reads Paul’s Jesus as exclusively celestial. He denies that Jesus had a brother named James. He dismisses the Gospels as historically useless. He denies the existence of Q. He dismisses the criteria of authenticity as completely invalid. And he claims to have found evidence for a pre-Christian Jewish celestial Dying Messiah tradition. Any one of these contested claims – if established - would alone be a significant contribution to scholarship. But to combine them all at once while calling for a fundamental paradigm shift in Jesus Research and historical methodology is to court controversy and, well, rejection.
  
  Unsurprisingly, Waters was unconvinced.......Carrier responded by pointing out that we don’t have enough evidence to falsify this argument from silence, noted that Waters didn’t provide any evidence of Jesus' historicity, and accused him of “ignoring” the scholarship on the Ascension of Isaiah....
  
  
  In the end, the audience asked questions, nothing was resolved, and we all went home. This was not an attempt for two ideologically opposed world-views and thought-systems to engage the other and negotiate common ground. No, it was two ideologically opposed world-views holding their own ground in parallel universes with "Jesus" as the central site of discursive conflict, illuminating once again, that "Jesus" is cultural capital in ideological struggles for power. But that's a post for another day

[John T]

Carrier may think he reduced the cost of Jesus by 15% in just 15 minutes but as the commercial goes on to says; 'that is not how it works, that is not how any of this works.'

Probability theory: The branch of mathematics that studies the likelihood of occurrence of random events in order to predict the behavior of defined systems...American Heritage

*****************************************

William Lane Craig debated Carrier years ago and pretty much killed Carrier's theorem back then.

Craig believes the evidence of the empty tomb is proof of a miracle.

Carrier does not believe in miracles therefore, Jesus was not raised from the dead.

But what is the belief/non-belief of miracles based on?
Statistics or religious belief?

Craig can point to scores of reports documenting modern day miracles (statistics).
Carrier refuses to investigate credible reports of modern day miracles due to his religious belief.

**********************
By definition, a true miracle can not be random because it is a deliberate action by the supernatural.

What is the probability of supernatural/miracles?
Answer: 100%.

What is the probability of hypocrisy built into Carrier's theorem?
Answer: 100%.

***********************

"There are three kinds of lies: lies, damned lies and statistics."...Mark Twain

[Bertie]

Thank you for this report.

In addition to Mr. Kirby's comments about Bayes Theorem, I have a sort of half-formed notion that the prior probability in Carrier's Jesus publications isn't providing the same level of utility as it does in "classic" Bayes Theorem applications like drug testing or trust in weather predictions. (I didn't find the prior probability in either OHJ or the Tacitus paper or the Josephus paper to be terribly impressive compared to the rest of those works).

But for me the big problem is one that we've discussed several times in the past: independence. Because that's not a problem with "historians being too stupid to do math" but rather "you think you're doing correct math but you're really not and so I can't trust your calculations at all, even if I granted you all of your assigned probabilities". Carrier is at least vaguely aware of the issue but I don't think he's consistently addressed it in his book. If a smart Christian apologist wanted to write a refutation of Carrier that would be an obvious route to take. There are forms of the probability formulae that account for partial independence, but historians are going to need guidance on how to use those, and how to think about independence when considering the types of evidence available to them, and of course we are probably beyond 6th grade math at that point and filling our history books with a lot more math than a history book using Bayes assuming independence of everything would have.

[Sheshbazzar]

He contends that every informal argument you've ever had about empirical subjects--every single one--could be represented in this form.

Then he gives a specific example of the claim found in Mark 15:33 and parallels, that the Sun went out for a full three hours during the crucifixion.

First, how typically does the sun actually go out? (relative prior probability)

Second, how likely is the evidence we have if the hypothesis is true and that happened?

Third, how likely is the evidence we have if the hypothesis is not true and it didn't happen? I.e., basically, how typically are such miracle claims just made up?

If you did this math, you'd find out that the probability that the sun went out for three hours is very small. You are doing this kind of reasoning in your head, even if you didn't formulate it in mathematical terms.

Perhaps the miracle (that the Sun went out for a full three hours) didn't happen. If we reject this 'event' then, the question remaining, is what might it be that lays behind such verses? What motivation? and what were the authors attempting to convey (if not an actual occurrence of 'miracles')?

It fascinates me that people who can get caught up in such arcane and subjective calculations as Bayesian probabilities, often remain almost wholly insensate to performing the simplest of '6th grade' mathematical calculations based upon the actual information provided within the Biblical texts.

In this case, of those 'full three hours' of darkness. Can seven of you perform the simple 6th grade math calculations, and agree as to exactly which 'three hours' of the year, month, week and day that these 'three hours' comprised? In what 'watch' in that year did this solar 'event' allegedly occur?
When did that year begin? When was the very first hour of that year? And on what day of the week did that year begin? At what hour?
Explain the methodology that you employ to determine such things. Its about time.


Sheshbazzar

[DCHindley]

Peter,

You lost me right after "Yesterday ..."

DCH