Tim Hendrix, a mathematician, recently published an inaccurate critique of my book On the Historicity of Jesus. This is my analysis of where he went wrong. Hendrix wrote a critique of my book Proving History: Bayes’s Theorem and the Quest for the Historical Jesus a few years ago, which I addressed last year. This year’s critique is of its sequel.
Minor Issues
Hendrix’s description of OHJ says some strange things. Hendrix says that chapter 1 “Surveys what constitutes relevant evidence. Dr. Carrier concludes the relevant evidence can be divided into four categories: (i) extra biblical evidence, (ii) acts, (iii) the gospels and (iiii) the epistles.” That’s not chapter 1. That describes chapter 7. Chapter 1 does outline the contents of the book (in a single page), which lists the evidence breakdown, but it does not “survey” what evidence counts or why. Most of chapter 1 is about the context of the debate, not the evidence deciding it. Hendrix correctly describes the other chapters, except for strangely describing chapter 6 as “Estimating how likely the two minimal historical hypothesis [sic] are a-priori.” That’s a weird use of the term a priori. Chapter six determines nothing a priori. It determines a conditional probability given certain specified background evidence. That’s called a posteriori.
In my analysis of his critique of Proving History I noted Hendrix does not seem to have an entirely solid grasp of English, and I found this hindered his ability to understand the arguments in my books. He frequently takes them as saying something they don’t, or not saying something they do. These strange descriptions may reflect the same issue. His description of chapter 1 does not appear to understand what the word “survey” means in English, for example. Likewise, the term a priori refers to logically necessary truths, such as that which can be determined from an analysis of terms alone (literally “relating to or denoting reasoning or knowledge that proceeds from theoretical deduction rather than from observation or experience”). As soon as you are drawing conclusions from observed evidence, you are no longer arguing a priori, but a posteriori. (See Wikipedia.)
I do not know why Hendrix confuses “a priori” with the Bayesian “prior probability,” other than perhaps unfamiliarity with the language and technical terminology. Prior probabilities are not a priori propositions; unless you are starting from an unconditioned prior, i.e. a logical demarcation of the probability space before inputting any background knowledge at all (other than logically necessary truths). Bayes’ Theorem is commonly not used that way. The prior probability used in real world applications of the theorem almost always takes into account some body of previous information, called “background knowledge” (the contents of b in the variable P(h|b)). I discuss this in detail in Proving History, and it’s covered in all standard texts on Bayesian reasoning. See also my second point in If You Learn Nothing Else.
Hendrix also shows signs of not having read the book carefully. For example, he says OHJ “does not state in any single place which formula is used for computing the probability of historicity,” yet it does: the Odds Form is shown on p. 598 in the calculations chapter (chapter 12), where I identify it explicitly, and present the equation. It’s even indicated on p. ix on the Table of Figures, as Figure “2. Bayes’ Theorem, Odds Form [ … p.] 598.” I even explain in n. 3 on p. 598 why I used that formula instead of the other that Hendrix instead proceeds with for some reason (which is just as valid, if more awkward). Since all the calculations in chapter 12 are shown and analyzed in the odds form, I have no idea how Hendrix can be unaware of this.
The Accumulated Error Argument
Hendrix starts by attempting to claim my method magnifies errors by a factor of five or even twenty. There are issues with the arbitrariness of how he determines this. But his argument does not apply to my method, so it’s moot anyway. Since my a fortiori estimates are all deliberately erring in favor of historicity, then by his own reasoning, my a fortiori conclusion should be over-estimating the probability of historicity by a factor of five or more. That’s the very point of my doing that. So that means the actual probability of historicity must be substantially less than 1 in 3, by his own reasoning. Which is exactly the conclusion of my book. Hendrix is thus making my argument for me.
Indeed Hendrix proceeds to show exactly that: estimates that we bias even slightly in favor of historicity will skew the end probability far more toward historicity than should be granted. Since that’s exactly what I do, and still I get only a 1 in 3 result, that is why Hendrix is arguing in favor of my conclusion, not against it. What he needs to do, if he wants to challenge that conclusion, is make a case for my historicity-biased estimates to be larger. And that’s precisely how any historian proceeds in any historical argument in history, whether aware of it or not. The extreme difficulty of arguing that higher estimates are at all plausible, translates into an equally extreme difficulty accepting a conclusion higher than the 1 in 3 my historicity-biased estimates entail.
If he could plausibly argue they should be higher, he should just do that, and not erroneously treat historicity-biased estimates as if they were mythicist-biased estimates. By making that mistake, Hendrix’s whole argument topples into what actually is a defense of the very conclusion of OHJ: any adjustment for errors in our estimates will make the a fortiori probability that Jesus existed lower, not higher.
The Trial Argument
Hendrix claims that “If your hair is found on the crime scene and you don’t live there, you are likely guilty of the crime.” I hope he is never a prosecutor, judge, or juror. Because that’s a disturbingly erroneous statement. Your hair can be at a crime scene for a thousand reasons, only one of which is that you committed the crime. Even if your hair is found in a wound, it could be transfer evidence, e.g. if the knife was taken from your kitchen, if the victim had borrowed your sweater and was wearing it, if you had hugged them earlier in the day, if they had brushed against you at the supermarket, and so on. Even if you had brushed against the killer at the supermarket. This is why when we can show any of this is the case or as likely to be the case as anything else, the hair becomes useless as evidence. It no longer is more likely to be there if you are guilty than if you are not. This is how all legal reasoning proceeds. In Bayesian terms, the likelihood ratio then washes out at simply 1/1: it weighs for neither hypothesis.
One correct thing Hendrix says here is that conspiracy theories, and any theory that presumes something is the case that has a low prior probability of being the case, depend on ignoring the resulting diminishment of priors. Hendrix gives the example of contamination at a crime lab producing the mistaken conclusion that your hair was at a crime scene, something that indeed would be very unlikely (usually). But that you hugged your friend in the morning, is not at all unlikely, even on prior probability, the more so if you have evidence you did so then or do so regularly. Thus, all likelihood ratios trend toward 1/1 the less determinative an item of evidence is of either hypothesis. We can’t escape this conclusion with a possibiliter fallacy that “maybe we are mistaken in our estimates of the probabilities” (see PH, index). That’s as unlikely as the lab mistake. Possibly does not get us to probably. “Possibly your hugging the victim in the morning is less likely than your having killed them” does not get you anywhere near “your hugging the victim in the morning is less likely than your having killed them.”
I explain the effect of adding assumptions to get a hypothesis to predict the evidence (it can reduce the prior probability, and quite rapidly as more assumptions are added) in Proving History (pp. 80-81; and index, “gerrymandering”). But when background evidence makes an assumption no longer an assumption but a highly probable event, e.g. when multiple parties attest that you often hugged the victim, then it does not reduce the prior. To the contrary, that background knowledge raises the prior probability of your having hugged them (thus transferring your hair to their sweater at some point) at least as high as the probability of your having killed them. Assuming that was the case therefore no longer reduces the prior probability. Because it is not an assumption anymore. It’s background knowledge. And the prior is always conditioned on background knowledge.
I also explain this fact extensively in Proving History. For instance, on pp. 220-21, I note that the absence of a court record from Pontius Pilate confirming the execution of Jesus is not evidence against historicity, because our background knowledge establishes an extremely high probability that all of those records would have been lost and unavailable even to someone in the second century, much less today. So arguing “we don’t have the record because it was lost” is not an ad hoc assumption we just invented to explain away the evidence. It’s not a conspiracy theory. It is not a “lab mistake” in Hendrix’s analogy. It’s the hug in my analogy. It therefore does not reduce the prior probability (by any amount worth noting). Because we know for a fact that the probability that that record would be lost is virtually 100%. Therefore assuming it was lost has no significant effect on the prior probability of historicity.
As we’ll see shortly, Hendrix repeatedly ignores this fact. He confuses background evidence with unevidenced assumptions—ironically while accusing me of doing that, when I don’t.
Defining Hypotheses
Hendrix shows again that he didn’t carefully read OHJ when he says “a difficulty Dr. Carrier does not address in On the Historicity of Jesus is the basic hypothesis of historicity is conflated with a particular theory for historicity and so it is not clear exactly what the basic theory of historicity or mythicism is.” Far from “not addressing” this, I address it extensively in OHJ, pp. 31-34 and 52-55 (and again on pp. 246-48, specifically addressing this “Complexity Objection,” under that very title!). I explain in detail why we need the terms I reduce them to, every single one; and I explain in detail why all remaining hypotheses can be excluded because they have vanishingly small priors.
Meanwhile, Hendrix does a worse job by trying to strip the hypothesis down to just “there once lived a man called Jesus who founded a religious group which stands in a causal relationship to Christianity today.” Many scholars argue Jesus neither founded nor intended to found a movement after him, yet nevertheless existed, and that his death only inspired a subsequent movement (which was actually founded by one of his students). So we can’t use the new hypothesis Hendrix proposes—it excludes too many historical Jesuses. It likewise includes too many historical Jesuses. There were certainly many men named Jesus who played roles in developing the Christian movement, even at its origin, as Jesus was a common name of the time. So that one existed in the original cult does not get us to “the guy they claimed was crucified and were worshipping” existed.
That’s why minimal historicity has to include all three terms I identify: Christianity was founded by men who followed a man at some point named Jesus, whom they claimed was executed, and then worshiped as a conduit to the divine. If you remove any one of those terms, you will be looking at the wrong Jesus, not the one we are interested in. If the Jesus Paul says they were worshiping and obeying the commands of was not the Jesus they were claiming had died and whose followers started the movement after his death, then that latter Jesus is not a relevant Jesus. It’s someone else.
It gets even worse when Hendrix tries to reduce the hypothesis to literally just “Jesus was a historical person.” Really. So. Which Jesus? There were hundreds of them. Including several in the early Christian movement. You can’t just state your hypothesis as “Jesus was a historical person.” You have to explain which Jesus you mean. That specification therefore becomes an inseparable part of the hypothesis. You can’t get away with “hiding” necessary elements of the hypothesis behind vague words like “Jesus.” Jesus ben Ananias? Jesus ben Jehozadak? Jesus the Sanhedrist? Jesus the High Priest? Jesus the Ship’s Captain? Jesus the Cretan? You have to specify. So I did. That’s correct procedure. Whatever Hendrix is doing is not.
That Hendrix thinks he is improving on my work by making it less rigorous and more misleading and ambiguous does not give me much confidence in his ability to correctly apply Bayesian reasoning to questions in history.
Completing the “Prior Probability Space”
Hendrix notes that by demarcating the hypothesis space with several conjoined terms, like “this Jesus was originally believed to have endured an ordeal of incarnation, death, burial and resurrection in a supernatural realm,” I am leaving some of the possibility space unaccounted for. For example, when we combine my minimal historicity with my minimal mythicism, there are still several hypotheses left over, so those two hypotheses I am testing do not logically exhaust the entire prior probability space. Contrary to what Hendrix claims, I explicitly acknowledge this in OHJ.
This is exactly what I myself point out, first on page 30:
‘Jesus was a historical person not mythicized’ [and] ‘Jesus was a mythical person not historicized’ … even collectively, consume a vanishingly small piece of the prior-probability-space (certainly less than a one in a million share). They can therefore be ignored.
And then for the five elements of my minimal mythicist hypothesis (pp. 53-55):
Unlike the minimal theory of historicity, however, what I have just said is not strictly entailed. If ‘Jesus Christ began as a celestial deity’ is false, it could still be that he began as a political fiction, for example. But as will become clear in following chapters … such a premise has a much lower prior probability … and a very low consequent probability … . Although I leave open the possibility it may yet be vindicated, I’m sure it’s very unlikely to be, and accordingly I will assume its prior probability is too small even to show up in our math. This decision can be reversed only by a sound and valid demonstration that we must assign it a higher prior or consequent, but that I leave to anyone who thinks it’s possible. In the meantime, what we have left is Premise 1. …
This same conclusion follows for Premise 2, which could also be false and mythicism still be true, but only on the alternative hypothesis that everything said about (and said to have been said by) Jesus was an outright and deliberate fabrication (or the product of such a deranged reading of scripture as to beg every question of why the movement would even have found followers), which again has a very low prior probability (certainly much lower by far than Premise 2), and a very low consequent probability …
Premises 3 and 4 could similarly be denied and mythicism still be true, so long as we posited that the founders of Christianity hallucinated the entire life and fate of an earthly Christ, or outright lied about it ever having occurred. But again, either possibility has an extremely low prior probability …
Finally, Premise 5 is already an effective certainty, as it is true even if historicity is true, and is so well verified in background evidence that its prior probability is as near to 100% as makes all odds. So the possibility of its being false will not be an issue. Since Premise 5 is certainly true, and the prior probability of any of Premises 1 through 4 being false and historicity still not being true is vanishingly small (certainly less than a tenth of one percent by any reasonable estimate), if I assign ~h to be the theory defined by Premises 1 through 5, I can safely assume that h entails historicity (given my minimal definition of historicity … ) and that these exhaust all relevant possibilities, and therefore I have a proper binary test, h and ~h, just two hypotheses to compare against each other, such that if one is false, the other is true.
Certainly, when framed like this, technically ~h (non-historicity) must also include all Jesus myth theories not defined by Premises 1 through 5 (that is, all theories of the evidence for Jesus that entail historicity is false and at least one of Premises 1 through 5 is false), but since their prior probability (even collectively) is surely less than a tenth of one percent (as I just reasoned), and their posterior probability not sufficiently high to make enough of a difference (especially in relation to minimal historicity), these theories share such a small portion of the probability-space occupied by ~h that they can simply be ignored. In other words, if ~h (as I have minimally defined it) is false, it’s simply the case that historicity is probably true.”
As all of that argument, ignored by Hendrix, entirely refutes Hendrix’s argument about demarcating the prior probability space, I should hardly need say any more on the matter. But as he seems to be confused about how this works, others may be as well, so I will take the time to explain what those paragraphs are saying and why it is correct.
Prior Probability Is a Relative Probability and Conditioned on Background Knowledge
If my minimal historicity combined with my minimal mythicism leaves a third segment of the possibility space left over, containing all other possible theories, but that section in its entirety is known on background evidence already to occupy a vanishingly small portion of that space (less than a tenth of a percent), then we no longer have to concern ourselves with that extra possibility space. We could. We could have three hypotheses and tediously continue the math for that third segment of the possibility space, but it would be a waste of time, as all we would ever get for it is absurdly low posterior probabilities, and there would be no significant effect whatever on the probabilities for the other two hypotheses I conclude with in the book. Because the effect had would be below the resolution of rounding that I employ and would thus be invisible.
The mistake Hendrix makes here is to forget that prior probabilities are relative probabilities, not absolute probabilities. Adding assumptions to a hypothesis only decreases the prior probability of that hypothesis if it increases the prior probability of an alternative hypothesis. So, for example, adding my term “this Jesus was originally believed to have endured an ordeal of incarnation, death, burial and resurrection in a supernatural realm” does not significantly reduce the prior probability of non-historicity because adding it only gives some of the prior probability space back to other non-historicity hypotheses. Adding it does not increase the prior for historicity. And what I then observe is that even the amount it increases other non-historicity hypotheses is negligible.
For instance, suppose we had no background knowledge, and demarcated h from ~h, or h1 from h2, as 50/50, even odds the Jesus we are asking about existed or not. Then we added a term a to ~h, making an h3 (so, ~h + a = h3), and then we made h2 into ~h when a is false (so, ~h + ~a = h2). And suppose this added term a itself also has a 50/50 chance of being true, something as likely to be true as not, we don’t know more than that. Then we would have a demarcation of priors equal to P(h1) = 0.5, P(h2) = 0.25, and P(h3) = 0.25, but h2 and h3 are both ~h, so P(~h) = P(h2) + P(h3) = 0.25 + 0.25 = 0.5. As you can see, adding the term did not increase the prior probability of h1. It had no effect on it at all. Hendrix somehow has not noticed this.
For a more apt analogy, if we return to Hendrix’s trial analogy, if we listed all the possible ways that your hair could be at the scene, and we then proceeded to show on background evidence that all the other ways it could be there were vastly less probable than a lab mistake, positing the lab mistake would no longer reduce the prior probability of your hair innocently being there, by any appreciable amount. It only would have that effect if we knew there were more likely ways of it being there. Like being guilty. But if, for instance, we surveyed legal cases and found in 99 out of every 100 cases the lab mistakenly placed a hair at a scene, positing that that happened in this case also does not produce any significant reduction in the prior probability of your being innocent.
Hendrix is trading on the assumption that labs almost never make such mistakes, that the prior probability of that is vanishingly small. That’s how we use background knowledge. This is exactly what I am doing when I rule out all other mythicist hypotheses, and end up with only one occupying half the possibility space (before inputting further background knowledge). In other words, after demarcating ~h into h2 and h3, I find background knowledge shows that h2 is like a lab mistake: vanishingly unlikely. That leaves almost the entirety of the 0.5 space that is occupied by ~h (which includes h2 and h3) occupied by h3 (as the portion of that space occupied by h2 is too tiny to even show up in my math). In other words, h2 is the analog to Hendrix’s lab mistake; not h3. That’s why I reject h2 and go with h3. Once again, Hendrix is making my argument for me.
Thus, if we eventually find that only 1 in 3 Jesus-like figures has in the past turned out to be historical, then 2 in 3 were not historical. There is no getting around that. Then, if all the ways Jesus can be not historical have vanishingly small priors except for “being believed to have endured his ordeal in a supernatural realm,” then adding “being believed to have endured an ordeal in a supernatural realm” to the hypothesis produces no significant reduction in the prior probability of non-historicity for Jesus. It remains 2 in 3. Because all the alternative ways for him to not exist have such small priors, that their effect is invisible at that resolution, showing up only several decimal places out—if we wanted to increase our resolution to so many decimal places, but there would be no point in doing that.
Hendrix thus forgets that prior probabilities are relative probabilities. He often acts as if he would insist the prior probability of a wealthy person having gotten rich by winning the lottery is the probability of winning the lottery, when in fact it is not, it is the frequency with which rich people got rich that way. If, for example, the only way anyone could ever get rich was by winning a lottery, the prior probability of having gotten rich by winning the lottery would be effectively 100%, even if the probability of winning a lottery were one in a million.
Analogously, Hendrix acts as if the prior probability of Jesus not existing because of “being believed to have endured an ordeal in a supernatural realm” is the probability of “being believed to have endured an ordeal in a supernatural realm,” when in fact it is not, it is the frequency with which relevantly similar non-existent people became historicized that way. If, for example, the only way any non-existent person was ever historicized was by “being believed to have endured an ordeal in a supernatural realm,” the prior probability of not existing because of “being believed to have endured an ordeal in a supernatural realm” would be effectively 100%, even if the probability of “being believed to have endured an ordeal in a supernatural realm” were one in a million.
But in this case, we have additional background evidence that narrows the field. For instance, though not every historicized person was “believed to have endured an ordeal in a supernatural realm,” every historicized mystery-cult savior god we know the full story of was (as background knowledge establishes: OHJ elements 31, 36, 40, 45, 48). And Jesus was a mystery-cult savior god (as background knowledge establishes: OHJ elements 13, 14, 18). Adding it therefore does not reduce the prior probability that Jesus didn’t exist. That’s simply the only way someone like Jesus (e.g. a historicized mystery-cult savior god) starts their existence. Other than for a few other ways that are so extraordinarily rare as to not even show up in our math at the resolution we are using.
Hence this is not like the lab mistake hypothesis; it’s like the hugging hypothesis. Those other ways Jesus could not exist are like the lab mistake hypothesis; and that’s why I reject them, because they vanish from the math, as even Hendrix would recommend (as that’s what he recommends for the lab mistake hypothesis). But we have abundant background evidence that this is the typical way mystery-cult savior deities start their existence; just as if we had abundant background evidence that we often hugged the victim. Therefore, Hendrix has his reasoning exactly backwards. And all because he isn’t reading OHJ carefully; and is forgetting basic details like these, of how a prior probability space gets demarcated.
So when we get later to the discovery that background knowledge establishes that no fewer than 2 out of every 3 people like Jesus didn’t really exist, we have our prior probability for ~h. And when we break ~h into h2 and h3 and discover our background knowledge establishes h2 as extremely unlikely, almost the entirety of the space occupied by ~h is then occupied by h3. And that’s why it’s the hypothesis I chose to test against historicity. When we look at how all those other non-existent people began, they began in various ways (e.g. political fictions, mythic pasts, ordeals in supernatural realms). When we look at the background evidence for Jesus, we can see that it is vanishingly unlikely that he began as a political fiction or someone who died in the distant past; that means almost all of the remaining probability space for ~h is occupied by the “supernatural realm” condition. Likewise if we proposed causes that have never been in evidence for anyone, or are even less likely than lab accidents—for instance, wholesale lying about Jesus having recently lived and died in Judea (which we can conclude has a vastly small prior from vast background knowledge regarding human and societal behavior).
Thus the “supernatural realm” condition does not reduce the prior probability that Jesus didn’t exist. It is in fact the only condition on which he could not have existed. Because all the others are extraordinarily unlikely. This is the consequence of prior probabilities being relative probabilities. They must be determined relative to all other competing hypotheses. Not in isolation from them. This is also the consequence of prior probabilities being conditional on background knowledge. Not in isolation from it.
Hendrix has missed all of this. He does not see how background evidence determines the result: e.g. that similar gods died in supernatural realms and had myths written of them placing their ordeals on earth; that the entire database of human and societal behavior renders the alternative mass-lying hypothesis vanishingly small before we even consider it further; etc. He confuses the effect of background knowledge on frequencies, e.g. his analogy of the lab mistake actually matches the non-existence hypotheses I reject as having vanishingly low priors (and thus he is actually making my point for me), whereas the elements I keep match the hugging hypothesis (as being demonstrably frequent for comparable religions of the time). And he does not see how relative probability entails the result: e.g. how when our background knowledge establishes only a 1 in 3 chance of historicity for persons of the same reference class, if the only way Jesus could be non-historical is to have been supernatural, then his having started supernatural has a prior probability so near to 2 in 3 as to make no difference.
Hendrix therefore has presented no relevant challenge to these conclusions.
Being Confused about Background Evidence
Hendrix ironically accuses me of being confused about what counts as background evidence, when he is the one who is. For example, he asks how the element of the hypothesis, that “subsequent” Christians believed Jesus historical, is in our background knowledge. It does not occur to him that the entire history of Christendom is in our background knowledge. We know second century Christians believed Jesus historical. That is not evidence pertinent to the hypothesis because none of those Christians had any access to the truth of the matter. So their believing that is as likely either way. Just as for Hercules, Romulus, Osiris, Inanna, Bacchus, Marduk, Asclepius, and so on. For all of them it is a true statement that “subsequent pagans believed they were historical persons.” We know that to near 100% certainty on background evidence alone. Before we even ask what evidence there is for or against that belief. So Hendrix cannot challenge this; it is already a certainty on our background knowledge, just as much for Jesus as for every other deity he resembles.
Of course, some second century Christians even attacked fellow Christians who were claiming Jesus didn’t exist (on earth), by fabricating evidence that he did (e.g., 2 Peter: OHJ, pp. 350-51). But I pulled that out of background evidence and placed it into the determining evidence (in chapter 8, though I end up assigning no weight to it either way). Because everything that is not in e is in b, and everything that is not in b is in e, without remainder. So what we put in each won’t matter, as long as we leave nothing out, and don’t put anything in both. Hence my remarks on p. 395 regarding how, even if the Gospels are 100% mythical, that fact alone has no net effect on the historicity of Jesus:
There is one important exception to this point: the Rank–Raglan data, which was used to construct our prior probability (in Chapter 6), because it can be correlated with enough examples to derive an actual probability that such data would accumulate for a real man. But we have already employed that evidence in our calculation (and only if we didn’t would we introduce it here: see Chapter 6 and the end of §2 in Chapter 12). Thus, the mythic character of the Gospels overall will affect our estimate of historicity. But only as much as it already has.
Notably, Hendrix shows no sign of having read that paragraph or even knowing it exists in the book. He even burns entire sections of his critique on an argument that is refuted by this paragraph (e.g. his 5.4.1). More evidence of his careless reading of OHJ.
Hendrix identifies no actual point anywhere in OHJ where I double count evidence as if it were in both b and e. In every case, I clearly demarcate what is in e, and do not use it again as if it were in b. Likewise the reverse. Indeed, he strangely says “The addition of additional elements to our basic theory is justified by essentially adding parts of the evidence to the background knowledge” yet “what is added is never stated.” This is false. I explicitly state every item of evidence I have placed in e. I even label it and assign a probability to it. Accordingly, anything I do not label and assign a consequent probability to is in b. I even explicitly discuss how I demarcate the contents of e and b on p. 59 (a page Hendrix seems not to have read). So it is false that I never state the demarcation. I am extremely clear and specific as to what’s in e. And by logical necessity, all other facts must be in b. Because the contents of e and b must exhaust all existing facts.
Indeed, by method of iteration (see Proving History, index), as soon as you output a posterior probability with any e, that e enters b in any further iteration of the equation inputting more evidence. And one could simply do that if they wished: start with a neutral prior (50/50), and put the Gospels entire in e (including the Rank-Raglan data), and generate a posterior probability, and then use that as the prior probability for the next input of evidence. The result will be identical. And I even say this explicitly in chapter 6, and show why mathematically either procedure comes out the same. It is therefore disingenuous of Hendrix to pretend otherwise.
Ignoring How the Reference Class Is Constructed
Hendrix has further erred here in not paying attention to how carefully I constructed the reference class I used to derive the prior probability of historicity for Jesus.
Hendrix says, “It seems plainly obvious to me at least that an early belief Jesus was historical in the Christian community…is easier explained if we assume Jesus was historical than if we assume he was not.” That’s refuted by every other example in the largest available reference class. In Chapter 6 I employ the Rank-Raglan class, detailed earlier in element 48 (OHJ, pp. 229-34), where I assemble fourteen persons, who exhaust all persons who fit that class (minus Jesus), all of whom were believed to be historical, yet none of whom were. Even at the most absurdly generous, we could maybe say 1 in 3 were (and that’s by literally just making up examples, assuming historicity without evidence). So clearly it is not the case that later belief in their historicity “is easier explained if we assume” they were historical. The evidence simply does not bear that out. Because none of them is plausibly historical.
I suppose Hendrix might be caught here in a chronological compression fallacy, confusing a hundred years later as being soon after an event, when even fifty years was an average human lifespan (element 22: OHJ, pp. 148-52). He is confusing modernity with antiquity, anachronistically imagining modern lifespans and documentation-access as existing two thousand years ago, and thus assuming anyone in the second century had access to ways to test whether Jesus existed a century before. When not only is that extremely unlikely on background knowledge alone, it’s unlikely on the evidence: for if they did have such access, we should have access to it as well, as surely it would have been preserved, or at least referenced. So the fact that they give us none, is confirming evidence that there was none.
I show this even more clearly in my discussions of Papias and Hegesippus, for example (in chapter 8.7-8). It is not possible that there were still people who knew Jesus personally in 100 A.D. who never in their entire lives wrote about it (or that no one had ever read or heard of anything they wrote). It is not even possible that there were still people who knew the Apostles personally in 100 A.D. who never in their entire lives wrote about it (or that no one had ever read or heard of anything they wrote). This would not count as evidence against the historicity of Jesus if we were to count it so (hence I would assign it no weight in my survey of extra-biblical evidence in chapter 8). But it certainly counts against any presumption that people in the second century had access to special data that makes their belief any more likely to be true. Their belief is therefore useless as evidence. It tells us nothing about whether or not Jesus existed, any more than the popular belief that Dionysus existed does. Hendrix is simply wrong to claim otherwise.
Hendrix rightly rails against basing probability judgments on undemonstrated assumptions. But he points to none that I base any probability on. All my judgments are based on demonstrated facts about the ancient world, thoroughly presented and documented (in chapters 4 and 5, consuming nearly 200 pages). Instead it is Hendrix who bases a probability judgment on an undemonstrated assumption: that second century persons had access to better evidence for the historicity of Jesus than we do. That is not in evidence. And it is substantially contradicted by the evidence we have. It is therefore a mere presumption, and a very unlikely one at that (see my remark above about Pilate’s records, for example). Therefore, that Jesus was not historical yet came to be believed to be historical remains as likely for him as for everyone else in his same reference class, like Hercules, Osiris, Dionysus, Moses, and so on. They were all non-historical yet came to be believed to be historical. In fact we don’t have any demonstrated instance of persons in the same reference class actually being historical. Thus, their actually being historical is not a better explanation of later belief in their historicity. No more for Hercules or Dionysus or Moses or Osiris than for Jesus.
Our background knowledge establishes that all non-existent persons (in that era and social system) sharing common characteristics with Jesus came to be believed to be historical. All of them. We must condition our probability estimates on that knowledge. Hendrix cannot evade this fact with armchair intuitions that are not in evidence or even contradict the facts of history. If we had Christians like Paul who within years believed Jesus was recently walking the streets of Judea, only then would Hendrix have a point—although it would not be a point about priors. It would be a point about likelihoods. For that would be evidence that Jesus existed. Precisely what we don’t have.
Using the Rank-Raglan Reference Class
Hendrix deploys a fallacy of credulity by saying that he can’t understand my argument that “if we only had the Gospels we should conclude Jesus most likely did not exist” because the Gospels portray Jesus as just like fourteen persons, and none of them existed. He says of himself, “I am not a historian, but I simply have great difficulties accepting this conclusion.” That’s strange. Because he claims to be a Bayesian. And you don’t need to be a historian, only a Bayesian, to recognize that when a hat contains fifteen beans and we know fourteen of them are black, the prior probability any bean you draw from the hat will not be black is extremely low. And prior probability requires us to treat all the beans alike. You can’t privilege Jesus. The prior odds that Hercules or Osiris were historical have to be the same prior odds that Jesus was. Because they are in the same hat.
Imagine Hendrix arguing that if all we had were the legends of the twelve labors of Hercules, we should assume Hercules existed; that if all we had were the legends of Osiris traveling Egypt, we should assume Osiris existed. This doesn’t make sense. Least of all because we have abundant evidence they didn’t exist; because we don’t “only” have their legends. We have earlier documentation of their supposed times and regions. Most gods and heroes, by far, did not exist. Yet had stories told of their adventures on earth, set in specific historical times. Any Bayesian worth their salt should have no difficulty seeing the point: if all other gods and heroes like that have such stories yet did not exist, then another god like that having such stories cannot be evidence they existed. To the contrary, we have to stick with the prior odds: usually, gods with stories like that, don’t exist.
That’s how background evidence conditions the prior. You can’t gainsay this by ignoring all this background knowledge and what it entails. No matter how much your intuition rages against the evidence, your intuition has to go hump. The evidence is king.
You simply have to give the same prior to Jesus that you would give to Moses, Hercules, Osiris, or any new god or hero we discovered who was painted the same way with similarly structured legends. Of course, there could be evidence that sets Jesus apart as special. Evidence that establishes he did exist, unlike all those others. But absent that evidence, if all you have is the same evidence you have for Hercules, Moses, Osiris, etc., then you have to accept the prior as all you know of their probability of existing. So you have to go on to look and see if we have special evidence for Jesus that we don’t have for Moses, Hercules, Osiris, etc. That’s what you do next. But until then the prior remains unchanged, until you find that special evidence, and use it to update your prior. Which then becomes your posterior.
Instead of doing that—the correct thing for a Bayesian to do—Hendrix becomes an even worse Bayesian when he deploys yet another possibiliter fallacy (see Proving History, index), stating that “if” the Gospel authors just mapped Rank-Raglan features onto an actual person’s story, then we’d have a historical person with those features. He even says “This seems like a perfectly sensible argument.” It is not. Because the question remains: How likely is that, rather than the reverse? Because you can say exactly the same of Moses, Hercules, Osiris, Bacchus, anyone in the set. Yet it would be illogical to say “because they might have been historical, and only had those features mapped onto them, therefore we should assume they were historical.” The correct question is: How often did people map those features to real people vs. non-existent ones? And the evidence shows the answer to be: Almost never (if not in fact actually never). Even actual persons who had some of those features mapped onto them (Alexander the Great, Sargon of Akkad) did not have more than half of them mapped to them, much less nearly all of them. In every prior case when someone has had more than half of them mapped onto them, they have turned out to be a non-existent person. This tells us that any new persons about whom that is the case, will also just as likely turn out to be a non-existent person. Because that’s what’s happened time and time and time and time again. Without any known exception, in fact.
That it’s still possible Jesus is the exception, the one actual person on whom that many attributes were mapped, is already accounted for in the converse probability. But we can’t change that probability from what the evidence shows it actually is (at worst 1 in 15, though I highly bias the estimate toward historicity by allowing it to be 1 in 3) merely because we are uncomfortable with that fact. We have to keep it where the evidence shows it actually is. To prove Jesus the lone exception requires evidence. Not presumption. Not armchair intuition.
Hendrix’s arguments for judging Jesus differently than other members of that set don’t work for Hercules, Osiris, Moses, or anyone else in the set, and don’t work for Jesus either. They, too, all have different features from each other—not all, for example, started life in a supernatural realm—yet still have the same prior probability of existing. The “they were different, therefore they aren’t the same” argument is a fallacy, one that would destroy all reference classes in the universe. Because everything is both different and the same. Literally everything that exists. Once we see that no more than 1 in 3 members of that set have historically existed, we must conclude that’s the prior probability any member of that set existed. What remains to ask is not whether 2 in 3 didn’t exist—that follows necessarily. What remains to ask is how. And that can vary. It does not matter if, for example, Asclepius did not start life in a supernatural realm. The possibility that Jesus also did not, is already included in our numbers: as an alternative hypothesis with such a vanishingly small prior for deities more like Jesus that it doesn’t show in our math at the resolution used in OHJ. Hendrix is thus wrong to claim I am not accounting for that. I am. And I explicitly say so. And he has no argument against the point.
Mucking Up the Reference Class
Hendrix makes more of these kinds of mistakes, leaning on possibiliter fallacy after possibiliter fallacy. For example, he tries his own “alternative class objection” (a ploy I already refuted in OHJ, under that very heading, on pp. 245-46), using a “recent person” class (a ploy I also already refuted in OHJ, under the heading of “rapid legendary development,” on pp. 248-52), not noticing that he doesn’t have any members of the required set: Recent persons who are Rank-Raglan typed (and indeed, by his own reasoning, “who were rapidly Rank-Raglan typed”). That set is empty (but for one member: Jesus). Therefore he has no data with which to construct a prior probability with this class. You can’t just make shit up. No data, no result. You have to move on. (Whereas, by contrast, that it “can’t” happen so fast is refuted by the cases of Ned Ludd, John Frum, and Tom Navy: OHJ, pp. 9-11 & 159-63.)
Hendrix similarly confuses the Josephan Christs Class (OHJ, pp. 245-46) with the Testimonium Flavianum, in which Jesus is not depicted as a Josephan Christ. Somehow Hendrix thinks that what makes a Josephan Christ (engaging in apocalyptic activities that evoke Joshua’s original conquest of Israel) is in the TF, when it is not. So he actually misidentifies the TF as belonging to a reference class it does not belong to. The TF never relates Jesus in any way that resembles the Josephan Christs (ironically, this includes the TF actually calling him a Christ; because Josephus never calls the Josephan Christs “Christ”; that’s not a word he ever uses in all his writings). The TF does not depict Jesus as an apocalypticist, or as a reborn Joshua, or as engaging in any apocalyptic messages or activities, nothing in fact that matched the messianic standard represented by the Josephan Christs (OHJ, pp. 67-73). This is, of course, yet one more reason why we know Josephus never wrote the TF. But even if we were to bizarrely suppose he did (contrary to all the evidence: OHJ, pp. 332-42), the TF does not describe a member of the Josephan Christ reference class. So Hendrix cannot use it as such.
Hendrix’s final sections are largely just full of speculative textual exegesis that he has no expertise in and that ignores nearly everything argued and all the scholarship cited in OHJ on the matters he attempts to critique. I find those sections too useless and uninformed to warrant any further response. Just read OHJ and, if you need more, the scholarship it cites on any given point. Likewise his concluding remarks are all based on the errors of his previous sections, and thus dissolve on noticing that.
Conclusion
Hendrix’s review is confused and lacks any critique of the actual contents of OHJ. It frequently ignores the contents of OHJ that already refute him; it identifies no actual errors of logic, mathematics, or fact pertinent to the actual argument in OHJ; and it makes arguments that actually reinforce the conclusions of OHJ. He errs in not understanding how my prior probability is constructed as it should be, as relative to all other competing hypotheses including those excluded by the two I test, and how my priors are conditioned on actual background knowledge amply demonstrated in OHJ, instead of the unevidenced assumptions and uninformed intuitions Hendrix tries to replace those facts with.
Hendrix uses false analogies (e.g. equating my ruled-in hypothesis as analogous to lab accidents, when in fact it is my ruled-out hypotheses that are analogous to lab accidents). He uses possibiliter fallacies (he assumes several times that when something is possible, e.g. that a dense Rank-Raglan matrix can be mapped onto a historical person, we should therefore take it as probable). He confuses historicity-biased probability estimates with mythicism-biased estimates. He tries to replace rigorously defined hypotheses with poorly defined and hopelessly ambiguous ones, and advocates that as an improvement. He ignores all my clear and careful statements about how I am demarcating evidence, and then accuses me of not saying how I am demarcating evidence and of taking no care in it. He rejects reference class sets that have many well-documented members, and tries to replace them with reference class sets for which he has no data at all. And he ignores background knowledge and tries to replace it with intuitions contradicted by that knowledge (e.g. of how often a dense Rank-Raglan matrix has been mapped onto a historical person; of lifespans in antiquity being half those of today and access to documentation of pertinent events almost non-existent; etc.).
In all, Hendrix’s critique is a travesty of error and confusion. He does not read carefully. He complains about lack of rigor then violates his own standards of rigor. He doesn’t understand the needs and requirements of historical argument. He locates no instance of my double-using evidence in e and b. He locates no instance of estimation error relevantly affecting my a fortiori conclusions. He locates no instance of any element of either hypothesis being improbable relative to all other variants of those hypotheses. And he presents no evidence that the prior probability of strong Rank-Raglan class members being historical is any different than I find at the a fortiori side—which is 1 in 3, not the much lower number he keeps repeating, which is my lower not upper bound—and he presents no evidence we should treat Jesus differently than any other member of that set.
All in all, a useless review.
Hi,
I think we have a communication problem in that as I read your response you believe that I have obviously not read (or understood) important sections of OHJ which answers my criticism. On the other hand I believe my review often directly addresses those sections you claim I have not read or understood and points out difficulties in your response — responding to your points above would therefore mainly consist of re-iterating arguments I have already covered in my review, and which I believe still stands as your response has not actually addressed them. On top of that I on the other hand think you often summarize my view incorrectly, sometimes to the opposite effect of what I intend, and you are therefore rebutting positions I do not hold.
In light of that I am not sure how we should best discuss our disagreements and I wonder if you have any suggestions?
Without addressing your main text I do want to ask you three questions:
Firstly, as I read your response you do not identify technical (mathematical) errors in my review. You sometimes disagree with my interpretation and assumptions, but the formulas in the review are sound and reflects your argument when that is intended? If not, could you please point out which computations are wrong?
Secondly, to paraphrase Jimmy from Better Call Saul: for reasons of my own sanity, can we agree that when you write:
Contrary to what Hendrix claims, I explicitly acknowledge this in OHJ.
(…)
(sections quoted from OHJ which I supposedly ignore:) “Finally, Premise 5 is already an effective certainty, as it is true even if historicity is true, and is so well verified in background evidence that its prior probability is as near to 100% as makes all”
(…)
As all of that argument, ignored by Hendrix, entirely refutes Hendrix’s argument about demarcating the prior probability space, I should hardly need say any more on the matter.
…then it is the case that the quoted section from OHJ that “entirely refutes [my] argument” and is “ignored” is in fact quoted on page 23 of my review (as are other sections supposedly ignored) and I discuss the argument in the following text?
I am wondering because to my mind “ignoring” an argument means not addressing it, but plainly I do address exactly the argument you quote even by quoting it myself and discussing what I see as it’s flaws using a computation?
The third thing I want to ask you about is regarding this quote:
Hendrix deploys a fallacy of credulity by saying that he can’t understand my argument that “if we only had the Gospels we should conclude Jesus most likely did not exist” because the Gospels portray Jesus as just like fourteen persons, and none of them existed. He says of himself, “I am not a historian, but I simply have great difficulties accepting this conclusion.” That’s strange.
The quote relates to p. 30 where I discuss that it follows symbolically from your assumptions in OHJ that
P(~h|Gospels.b) = 93.75%
That is, if we assume only the Gospels and b (and none of the other evidence like the epistles or extra-biblical evidence and so on) then there is a 93.75% chance Jesus did not exist. You are right I am not refuting this position in the paragraph, but I was simply taken aback by it because to my mind this conclusions seems to be the most surprising of the entire book. I therefore want to ask you this: Can you confirm that you have come believe the above conclusion is true, that on the Gospels (and b) alone there is a 93.75% chance Jesus did not exist?*
(*using the most likely estimates of probability).
“I believe my review often directly addresses those sections you claim I have not read or understood and points out difficulties in your response.” And as my response demonstrates, it does not. In fact, in each case I document, not only does your review not respond to what my book says, it shows no signs of even knowing that’s what my book said. So your belief is not in alignment with reality. And that may be the problem.
“Firstly, as I read your response you do not identify technical (mathematical) errors in my review.” Because if there were any, they weren’t relevant. If you can’t even get the facts right, what math you do with your incorrect facts is moot. For example, you incorrectly describe my historicity-biased estimates as mythicism-biased estimates. All the ensuing math is therefore irrelevant. You are describing the wrong thing, and thus applying entirely the wrong math.
“I am wondering because to my mind “ignoring” an argument means not addressing it, but plainly I do address exactly the argument you quote even by quoting it myself and discussing what I see as it’s flaws using a computation?” No, you don’t. As I meticulously show, whatever you think the quoted text says, it’s not what you then go on to argue. You never once actually address the actual import of that quote, and I show this in detail above.
You instead claim I never said things that in fact I said repeatedly and in detail, and you instead never once even acknowledge the fact that I admit to there being additional hypotheses; you never once even knowledge the argument I made that their priors are vanishingly small and therefore can be ignored; you never once even acknowledge that as I have constructed the model, increasing the priors for those ignored hypotheses would not affect the prior probability of historicity in any way—because I condition the latter prior on the data, and then the converse probably automatically follows for ahistoricity; and you completely ignore my detailed explanation that once we’ve done that, it remains only to demarcate that ahistoricity probability space (which is automatically and undeniably the converse of the space occupied by historicity) among the available theories of ahistoricity; and you never once address any of my arguments for all those available theories having a vanishingly small portion of that space, leaving only one theory over, which is thus the one I explore. You don’t even show any sign of even having understood that this is what I did or what I argued. You certainly never rebut a single point of that argument.
And that’s just one example. My article documents many others.
“That is, if we assume only the Gospels and b (and none of the other evidence like the epistles or extra-biblical evidence and so on) then there is a 93.75% chance Jesus did not exist.” That is only my a judicantiori margin. I actually conclude its closer to 67% (rather than 93.75%) on historicity-biased estimates. Hence the one is my lower and the other my upper bound. A point you also continually ignore.
But yes, I myself do believe that if we found today any random new “worshipped savior demigod” in antiquity, who had biographies like the Gospels, because they are in turn like the biographies of every other Rank-Raglan hero known, we should conclude the subject of them very likely (e.g. circa 93%) did not exist. And we should conclude that because that’s been the case over a dozen times, and moreover, in not a single known case has it ever been otherwise.
Your intuition might beat against those facts like an ox against the goad. But the facts always win. The fact is, everyone else in that set didn’t exist. Jesus is in that set. Therefore, on prior probability, Jesus didn’t exist either. We need evidence to turn that around, just as we would need for Hercules, Osiris, Romulus, Adonis, Dionysus, Jason, Moses, Joseph, or anyone else in that set. You can’t declare Jesus the exception to the evidenced rule without evidence that he is. Your intuition cannot replace the facts. If your intuition contradicts the facts, your intuition is wrong.
Which is why we need to argue from the actual facts, not “what we feel is true” irrespective of the facts. Human intuition is often catastrophically at odds with reality. I would have hoped a Bayesian of all people would have learned that by now. As virtually every problem Bayes’ Theorem has solved (from the famous mammography case and beyond) has consisted of demonstrating the pervading intuitions of even experts are routinely wrong—as when doctors often intuit the wrong probability of a patient having an ailment on a positive test result, an error Bayes’ Theorem corrects, by forcing them to replace their intuitions with facts—and the inevitable logical consequences of those facts.
No one who knows what a base rate is, can disagree with the conclusion that Rank-Raglan biographies signal ahistoricity, and do so to a probability beyond 90% (or at the very least beyond 65%).
Hi again,
Well, I think you get the central points of my review wrong and all I can really do is to invite a reader to read both texts and see for himself if that is the case. For instance I believe the argument you claim I ignore, regarding the extra elements in your myth-theory, is addresses in quite great length from page 23 onwards in my review. For instance, on page 26 I agree one can define the background evidence such that the probability of the five-point myth-theory is 1 given a historicity, but my point is that this has to be accounted for when computing the prior — something the Rank-Raglan reference class obviously does not do in my opinion.
I realize you disagree with what I have to say (in my opinion, because your response misunderstands what I say) but I don’t think you can say I “ignore” this argument — I even quote it verbatim. If I am ignoring a specific argument, can you perhaps state what it is symbolically?
Thank you for confirming that on your view Jesus nonexistence is nearly guaranteed on just the Gospels:
P(~h | gospels . b) = 93%
Regarding if this should be 93% or 66%, as a point of clarification, OHJ frequently describe the 93% as the most realistic estimate and not as a mythicism-biased estimate which is why i mention the 93%. See for instance p. 375 and 596.
Nevermind, regarding your point that:
I myself do believe that if we found today any random new “worshipped savior demigod” in antiquity, who had biographies like the Gospels, because they are in turn like the biographies of every other Rank-Raglan hero known, we should conclude the subject of them very likely (e.g. circa 93%) did not exist.
I would like to point out that for any “random” demigod we don’t have the entirety of church history in the background information as we do for Jesus… So your example should probably be more like: Suppose a new random demigod turn up about which we got the RR criteria and about which we also have church history describing the random demigod as having lived fairly recently.. (and so on). I at least would conclude that demigod likely did exist, but I don’t claim this is anything more than my intuition.
I will address your response in more length at a later point, however I have a few more questions of clarification: Your use of reference classes to estimate the probability of specific events, like the prior probability of Jesus existing, falls into what’s known as the “reference-class problem” according to all sources I am aware of, see for instance
https://en.wikipedia.org/wiki/Reference_class_problem
http://philrsss.anu.edu.au/people-defaults/alanh/papers/rcp_your_problem_too.pdf
Do you believe the reference-class problem does not matter or that, well, you get around it somehow? in which case how? (whats the computation?).
Speaking of reference classes, in general, how should we use a reference class to estimate a prior probability. Is it:
P(A|B) = #(Elements that match A and B)/#(Elements that match B)
or something else? if so, what?
In my review I claim reference classes can’t be used in the manner you do, to compute the prior probability of specific events like Jesus existence: Computing prior probabilities of unique events in this manner is not found in any textbook about probability theory because it can only be considered accidentally correct.
do you know of a textbook of probability theory/statistics that says we can use reference classes in this manner and embarrass me with a smack-down for this argument?
As I touched upon in my previous post we have reached a kind of stalemate where you believe I don’t understand (and therefore does not address) important points of OHJ, and I believe something similar about your response. As I think we are really discussing fairly trivial points about probability theory, I don’t think this is necessary. For whatever it is worth I would like to say I am open to a more interactive form of discussion which I think might be more productive if this could be arranged.
I’m content to let reasonable people compare what I say with what you said. I know who they will conclude is correctly describing things.
As to your repeating the fallacy, “Suppose a new random demigod turn up about which we got the RR criteria and about which we also have church history describing the random demigod as having lived fairly recently,” (a) we don’t have that for Jesus (not a single person attests to his having “lived fairly recently” on earth outside the RR myths in the Gospels; no non-mythical document asserts that until almost a hundred years, and at least two average human lifespans, after the purported event; and from then on the sources disagree on what decade or even century he lived in, and exhibit no access to any evidence of his ever having lived on earth other than the mythical RR Gospels) and (b) your reference class is empty (unless you want to include the examples of Ned Ludd and Tom Navy and John Frum, or even the Roswell aliens, all of whom became asserted to “have lived fairly recently,” indeed within just 40 years of their supposedly having done so, but never did—but if you count that as precedent, you lose the argument straightaway).
You can’t use empty reference classes. Certainly not when I have a reference class that contains fourteen actual members!
You aren’t acting like a competent Bayesian here. You are acting like an apologist desperate to deny the facts by replacing them with feelings.
Analogy:
I have a test for syphilis (ahistoricity). It has correctly identified syphilis in all fourteen previous cases, with corroborating tests verifying the fact. It therefore has a false positive rate of circa 7% on direct information, or allowing for statistical flukes, not reasonably any higher than 33%.
You then come along and insist that because the test in this case is applied too soon, it has a higher false positive rate. The scientific community asks you for your evidence that the rate is different when the test is applied in that window of time. You have none to present them. They ask you, then, on what facts you base your assertion? You admit, you have none. They then show you that other syphilis (nonhistoricity) tests applied as soon have no worse a false positive rate (the cases of the Cargo Cults and the Luddites and the Roswell incident and so on), therefore what facts actually exist, do not support your insistence upon a higher false positive rate. They have evidence refuting you. You have no evidence supporting you.
So why do you persist?
The test is verified. The data supports my margins of error. You have no data supporting any other.
Hi,
I can’t help noticing you didn’t address my question about the reference-class problem. I am particular interested if you have a technical reference that indicates reference classes can be used for one-off events like you imagine and, in general, how you define a reference class formally? If, say, we have the prior:
P(h|b)
Where b contains many pieces of quite specific information (as in our case), what then would be the formal definition of a reference class in this context and how do we use it to assign probabilities in general?
Regarding your reply:
we don’t have that for Jesus (not a single person attests to his having “lived fairly recently” on earth outside the RR myths in the Gospels;
But we *do* have the church history (and all the other information in b) for Jesus. My point is that the probability Jesus existed is not just that of a random demigod that matches the RR criteria, it is the probability that a “random demigod” that matches the RR criteria *and a whole bunch of other stuff including church history* existed.
Regarding your medical test. Well, that example is very different than Jesus. Firstly, you are here stating what the probabilities are, and secondly, for medical tests we are not considering one-off events (like Jesus existence with rich background information) but rather repeatable experiments where humans are assumed to behave roughly similar when subjected to the same treatment. Once again, I invite you strongly to read the references to “the reference class problem” to understand this use of reference classes is considered highly problematic.
So why do you persist?
Well, a big fat reference to a textbook on Bayesian statistics that uses reference classes to compute prior of events such as Jesus existence (i.e. one-off events where we have a great deal of background information) similar to how you do would go a long way to shut me up. You might have noticed I have been asking for such a reference for a while :-).
Every “historical figure” passing the Rank-Raglan test. Fourteen pieces of specific information. How we use this is carefully explained in detail in OHJ.
Not as having lived “fairly recently.” You are deploying an equivocation fallacy here. At one point you want “recent” church history attesting to Jesus (of which there is none; not even Paul places him on earth; neither does Clement, Hebrews, or even 1 Peter), because that (you argue) would set him apart from the Rank-Raglan class. But that set is empty (no examples to test in the RR class) or has members who were ahistorical (founding heroes Ned Ludd, John Frum, and Tom Navy). So that doesn’t get you anywhere. So then you want “any” church history attesting to Jesus. Which of course exists. But that parallels all Rank-Raglan members (who all have that kind of “history attesting” them), and therefore gives us no data privileging Jesus over them. So you have no logically valid argument here.
That’s true of every single member of the RR class. Therefore, it’s irrelevant. It’s like saying that people who get tested for a disease have different hair colors and only some had stories about them in a newspaper once, therefore they don’t make up a common reference class.
No, I’m deriving the probabilities from prior applications of the test. Just as I explained in my last comment. That’s how this gets done. For disease tests as well as anything else.
Every test subject in a lab is a “one-off” event with their own unique personal history with rich background information (and their own unique physiology and body chemistry and travel history and gut flora and so on). That’s irrelevant data. Jesus is no more a “one-off” because he has his own story that differs from others than a medical subject is; or any other member of the RR class is–they all have their own special stories. The relevant information is what they have in common. That correlates with an observable trend. If it didn’t, we’d have found many members of the RR class existed. That we found none do strongly indicates a correlation. I allow that correlation to be as weak as 1 in 3 predictive of ahistoricity, even though it actually is as strong as 1 in 15 predictive of ahistoricity.
This is how all statistics works. We find correlations between shared features (Republicans, Americans, black people, violinists who eat iced cream, and so on). All the other special facts about them are irrelevant. Until we know those special facts indicate a different correlation (e.g. discovering a Republican is a Libertarian will predictably alter the frequency of their opinions on certain subjects, in a way their hair color will not). So you need to find such a correlation. You have failed to do so. And you don’t get to invent them out of thin air. Your attempt to find one in “fairly recent attestation” is a failure because there is none. You have to equivocate about what “recent” means so much that the distinction between Jesus and other RR members and ahistorical founding heroes vanishes. You can’t work with sets that are empty. I have a set with fourteen members in it, who highly correlate with a common outcome. What set do you have? How many members? What correlation does it produce relevant to this discussion? (And your answer has to acknowledge that its a set containing RR heroes, because Jesus is one, and what properties non-RR heroes have is not pertinent to predictions regarding what RR heroes correlate with.)
I’m astonished I have to explain to you how statistics works. Do you seriously think “unique histories” negates all statistical tests and polling of people in history? You seem to be arguing against the entirety of the field of statistics. That’s a ridiculous length to go to to avoid admitting the truth here.
Hi again,
What is the html tag for making quotes?
First off, I don’t think you answered my question regarding how we formally define a reference class and use it to assign a probability.
I don’t disagree Jesus matches the RR criteria (as I have said several times), but there is *more* information about Jesus. You are right this point applies to many statistical situations — but thats my point, we are discussing a well-known issue (the reference class problem), and I would hope you would at least acknowledge that literature, especially when you wish to claim I am misunderstanding basic points in statistics. If I am, you should be able to provide a textbook on Bayesian statistics which shows your use of reference classes is valid.
On the point of me equivocating on how “recently” Jesus lived, let’s clear this up. According to modern historians Mark was written around year 70, about 40 years after Jesus lived. Where does this information go? (background information or not?). Where does the information go that people in (say) the second century believed Jesus had lived in the first century? (background information or not?)
Let’s take another tack on the issue: I don’t know what you would say the prior probability Socrates lived is, but let’s say its 50% and information like Plato pushes his historicity up higher.
Suppose I sit down and write a “Gospel” about Socrates where he matches more than half the RR criteria (a bit like the Gospels). We can both agree that information is completely irrelevant for his historicity, but on the other hand Socrates now matches the RR criteria and so I could compute a prior of 94% he did not exist *based on this information alone*.
What would the argument against this look like? Obviously, a single document from 2016 would be irrelevant even if it described Socrates as matching all RR criteria, but that chronological information would be in the background information (it would be equivalent to the church history). So in this example the background information WOULD contain additional information about Socrates(/Jesus) which was relevant (you can probably think of many other reasons why the information is irrelevant but I think they would also involve background information in some way).
My point is that in this example, the background information certainly can’t be ignored and boiled down to the RR criteria — which shows that as a rule we should take the background information, including chronology, into account.
You can argue we don’t have any relevant background information about Jesus except the RR criteria, that Jesus is in no relevant way different than the RR heroes, but I think many others would disagree. For instance does Moses interact with named historical persons like Jesus? Is that relevant?
Notice I could use your arguments above: But Socrates DOES match the RR criteria (according to this document), and you would no doubt object similar to how I do: But there is OTHER information, like this is a SINGLE document, like it was written in 2016, etc. etc. in the background information that you MUST take into account.
You would properly also point out I should provide a reference for my use of reference classes from statistics, or otherwise it was not very convincing ;-).
Also note how all these troubles would go away if we took your advice on p59 of OHJ and treated the RR information as evidence because it causally depended on our hypothesis: As evidence, my silly document would be equally easily explained regardless of Socrates existence.
Hope you have a good weekend and thanks for keeping the comments section open. I still hope we can discuss this in a more interactive medium someday.
I’ve answered all these questions several times now.
I’m not going to repeat myself. I’ve discussed not only here but in detail in my book all of this:
(1) The Gospels place Jesus in a set strongly correlated with ahistoricity, in just the same way as all the other members of that set with the same kinds of stories about them, and if you want to show he is different (by appealing to other things about him) you have to show me a set he belongs to that combines members of both sets and yet correlates different with ahistoricity, and you have none (no set with any data in it); I have a set with data in it. Data wins. You can’t just “presume” a difference matters. You need examples of it actually mattering for RR heroes. Otherwise, you are just speculating. I’m not speculating. I’m sticking with the actual documented facts.
(2) I’ve documented average human lifespans of the time (48 years) and poor access to records and the failure of any author to reference any sources other than the Gospels etc., as well as that the only time Jesus is affirmed historical outside an RR myth is in the second century A.D. And I’ve fully addressed the entire “rapid legendary development” and “different reference class” arguments in the book. I’m content to let all my actual information compete against your repetitious intuition and let the public decide which is more relevant or persuasive.
(3) I fully address the Socrates comparison in the book. That you once again don’t even seem to know that is starting to piss me off. I should also not have to explain to you that Socrates isn’t in the RR hero set. Or how the considerable evidence for his historicity would overwhelm a 1/15 prior against his historicity easily. Read. The fucking. Book.
And if you missed how different historical periods no longer pertain (whether we now, two thousand years later, convert Socrates into an RR hero has no relevance to the question of his historicity; just as the frequency of ahistoricity for RR heroes today has no relevance to the frequency then, any more than the frequency of wealthy musicians today has any relevance to the frequency of wealthy musicians then), you might want to read another book you claim to have but clearly didn’t: Proving History, pp. 245 and 250-53.
Stop this desperate appeal to intuition over fact, ignoring everything I say, and insisting on irrelevant demonstrations. The correlation I rely on exists. You have no evidence that it differs for Jesus. That’s the end of this argument. Unless now you intend to delusionally deny these facts. But I am not going to waste my time arguing with your delusion.
Hi,
I’ve answered all these questions several times now.
I have to disagree. I believe I have asked about 3 times on this thread how you formally define reference classes and if you can provide a citation for a similar use of reference classes (lots of background information) from the literature on Bayesian statistics. I think this is of some important since I have provided references for articles that discuss exactly the problems I bring up (the reference class problem).
(1) The Gospels place Jesus in a set strongly correlated with ahistoricity, in just the same way as all the other members of that set with the same kinds of stories about them,
I agree with your first point: If we define a set hero-types that matches at least half the RR criteria then Jesus is in that set along with other (fictional) characters.
There are two problems: The first is that *we have more information about Jesus*. That is, we can define *other* sets containing Jesus and which correlates differently with historicity/ahistoricity. This is exactly the core element of “the reference class problem” (see the previously cited article by A. Hajek).
The second problem is that this business of defining sets (reference classes) and compute probabilities from the frequency of these sets is not something that mix well with the ideas behind Bayesian statistics — that’s why I keep bringing up you should look for a reference from the Bayesian statistics literature that does something similar or simply read some of the references I gave you on the reference-class problem. The basic issue is that on a Bayesian view we should more naturally ask: How probable is it that Jesus, with all the specific information we have about Jesus and the Gospels, would later have his stories constructed to contain the RR criteria (on historicity or not). That’s the kind of question Dr. Rank brings up himself and where he (as I read him) believes this is about equally probable on both historicity and myth. You can disagree with Rank and believe he has not thought hard enough about the subject, but that’s a different kind of discussion.
and if you want to show he is different (by appealing to other things about him) you have to show me a set he belongs to that combines members of both sets and yet correlates different with ahistoricity
Why would a reference class I propose have to contain members of your class as well? I could just as well say: You can’t use the Rank-Raglan class because the combined class (your class and whatever I might propose) is empty. Can you see the problem? Once again, the issue is that using reference classes we get into these weird issues and ambiguities, see “the reference class problem”.
You can’t just “presume” a difference matters.
Well, can you just “presume” it does not? I want to point out I am for instance citing Dr. Rank who seems to believe there are differences that makes the Rank-Raglan class uninformative for historicity for Jesus. I think I am in a bit of a catch 22: If I bring up examples of different reference classes to highlight the ambiguity of the method, you dismiss them because “they don’t contain members of both sets” (which I don’t consider a valid argument), and when I bring up problems with reference classes (their fundamental usage and ambiguity which, as evidenced by my sources, is just well-known) you dismiss that by saying I should give an example of a reference class… That’s a bit of a no win and I don’t think that how the burden of evidence works.
(2) I’ve documented average human lifespans of the time (48 years) and poor access to records and the failure of any author to reference any sources other than the Gospels etc., as well as that the only time Jesus is affirmed historical outside an RR myth is in the second century A.D.
The point I would come back with is that this situation is still different than (say) that for Moses: For Jesus we *have* stories about him which places him in history fairly recently (The gospels, about 40-50 years prior, and the church history, about 100 years prior). I agree that this is not like a source that says he lived 10 years ago in recent memory, and that it has to be taken into account that the Gospels is not just sober history, but I think it is a relevant difference compared to Moses or Hercules. You can disagree and cite your own greater authority as a PhD in history but my point is simply that if (say) another historian believes this difference is importance that would undercut the use of RR criteria.
(3) I fully address the Socrates comparison in the book. That you once again don’t even seem to know that is starting to piss me off. I should also not have to explain to you that Socrates isn’t in the RR hero set. Or how the considerable evidence for his historicity would overwhelm a 1/15 prior against his historicity easily. Read. The fucking. Book. And if you missed how different historical periods no longer pertain (whether we now, two thousand years later, convert Socrates into an RR hero has no relevance to the question of his historicity; just as the frequency of ahistoricity for RR heroes today has no relevance to the frequency then, any more than the frequency of wealthy musicians today has any relevance to the frequency of wealthy musicians then), you might want to read another book you claim to have but clearly didn’t: Proving History, pp. 245 and 250-53.
(My bolding). I think the bolded section is very interesting. The issues you bring up all revolve around how additional information (like the RR Socrates stories are written in 2016) can and in this case obviously should influence our use of the RR hero class for Socrates: Background information matter at least in this case.
But that means that in general background information is of importance, and thus when we observe that (say) Socrates, Hercules or Jesus by some information is placed amongst heroes who match more than half the RR criteria, we should immediately consider if there is additional background information that should influence how we use that information; again, as the quote by Rank would seem to imply, some historians believe this is the case. You can disagree and say: No, all background information can be reduced down to just the RR criteria and everything else does not matter, but that’s your opinion of the evidence and not something that follows from any sort of statistical argument.
Fully answered, multiple times. I even have an entire section on it in the book.
Analogy:
If Jesus is a Right Wing Libertarian, comparing his opinions to Libertarians as a whole is not going to get you correct results when you have results for Right Wing Libertarians. Therefore, when you know Jesus is Right Wing, you can’t leave “Right Wing” out of any reference class you are generating data from. That’s “leaving background evidence out,” a no-no for honest Bayesian reasoning. If you want to insist that Jesus is different from other Right Wing Libertarians because he is also from Idaho, you can’t just say “people in Idaho think x, therefore Jesus thinks x,” you have to look at what Right Wing Libertarians in Idaho say, and only if that is different can you say Jesus is different.
This is why you cannot generate a set that ignores that Jesus is in the RR set and attempt to erase the effects of his being in the RR set by “leaving it out,” and “leaving in” only this other set membership you conjured up. Because that’s leaving data out of background evidence. So now you have to put it back in: Jesus is also in the RR set. What is the effect of now adding that information? Exactly the same as what I show in the book.
The only way you can change this is by finding a set whereby being an RR hero has different effects for Jesus than for the other members. You have no data to do that with. So that’s the end of this.
Another way to put it is: we could, if we wanted, put one single item in b (that Jesus is a named person in history), then add one single item in e (Jesus was a godman), and see what the effect of that is; then add one single item in e (people a human lifespan later believed Jesus was historical) and see what the effect of that is; and then add one single item in e (Jesus was an RR hero from the first moment any earthly stories were told of him), and see what the effect of that is. By the end of that process, all those items in e have entered b. (This is, again, all explained and mathed out in the book.)
So there is no way to avoid the effect of his being in the RR class by trying to call attention to his being in the “people a human lifespan later believed Jesus was historical” class. You have no data for that class anyway. You certainly have no data for the effect of being in both classes (both a Right Wing Libertarian and in Idaho).
So you have no argument here. No data, no result.
I have data, you do not.
That’s the end of this argument. All your obfuscating about irrelevancies cannot dodge this.
Yes, it’s possible a Right Wing Libertarian thinks differently in Idaho than everywhere else. But that it is possible is not data. You have to stick with what you know. And that’s the national opinion polls for American Right Wing Libertarians. If you ever get data for the Idaho subset, then you can enter it and change the results. Until then, you have to work with what you know. That’s how epistemic probability works. That’s the whole point of Bayesian reasoning: calculating what the probability is given the limited knowledge you have. That “if we knew something else, that probability will change” is true. But still doesn’t permit changing the probability without that new knowledge.
I discussed this fact in elaborate detail in Chapter 6 of Proving History. Once again, you act like you never read that.
The bottom line is, I am actually deriving my epistemic prior from all the data that’s in b. You want to invent non-existent data for mere possibilities and somehow alter the outcome…from whatever your imagination invents as the required data. I’m using actual data. You are inventing data. That’s the difference between us. And on that difference, only one of us is being reasonable.
Hi again,
If Jesus is a Right Wing Libertarian, comparing his opinions to Libertarians as a whole is not going to get you correct results when you have results for Right Wing Libertarians. Therefore, when you know Jesus is Right Wing, you can’t leave “Right Wing” out of any reference class you are generating data from. That’s “leaving background evidence out,” a no-no for honest Bayesian reasoning.
Completely agree: All background evidence must be taken into account and can influence our inferences; I have never suggested otherwise.
If you want to insist that Jesus is different from other Right Wing Libertarians because he is also from Idaho, you can’t just say “people in Idaho think x, therefore Jesus thinks x,”
Agree once more. But here is the rub: the same logic, I can’t just say: “Jesus is a Right Wing Libertarian, Right wing libertarians think x, therefore Jesus think x”. Or for a more relevant case: “Jesus is a RR hero. RR heroes exist (with probability 6%). Therefore Jesus exist with probability 6%”. We have more information about Jesus that should be taken into account. As you very rightly start out by noting, background information should not be ignored.
This is why you cannot generate a set that ignores that Jesus is in the RR set and attempt to erase the effects of his being in the RR set by “leaving it out,” and “leaving in” only this other set membership you conjured up.
Ah, that might explain why you object so strongly. I never suggested we should “leave out” any RR information, by all means let’s keep it there. I am just saying it has to be seen in light of all background information.
Jesus is also in the RR set. What is the effect of now adding that information? Exactly the same as what I show in the book.
But that prior is:
P(Exists| “Match at least half the RR criteria”)
not
P(Exists| b)
where b is all background information including the RR information. Do you see the point?
The only way you can change this is by finding a set whereby being an RR hero has different effects for Jesus than for the other members. You have no data to do that with. So that’s the end of this.
Well, this is where you really need to look in the literature and come up with a reference that supports this reasoning. What you observe here is (correctly) that all our background information b only really matches one person, Jesus, and so it isn’t useful to construct a non-empty reference class from. But that’s a problem about reference classes and finite frequentism, the reference class problem, and it certainly is no excuse for ignoring that information. I am not sure you agree with me or not, but this whole business of finding a “set” of literary characters Jesus belongs to and approximate his existence using the members of this set (reference classes) has absolutely no fundamental status in Bayesian statistics; under a Bayesian view of probabilities, there most likely (as in the case for Jesus) is no such set because that’s not what probabilities refer to.
Sorry to sound like a broken record, but if you disagree with me on that point and believe there must be such a set you really got to start by finding a reference from the literature that agrees with you (and is not Proving History). It certainly is not Jaynes probability theory or Earmanss Bayes or Bust.
we could, if we wanted, put one single item in b (that Jesus is a named person in history), (…) then add one single item in e (Jesus was an RR hero from the first moment any earthly stories were told of him), and see what the effect of that is. By the end of that process, all those items in e have entered b. (This is, again, all explained and mathed out in the book.)
Indeed! But that’s my point about the quote by Dr. Rank. As I interpret that quote, it is saying the probability that Jesus being made to match the RR hero class is equally large on historicity or myth because in both cases the Gospel author was telling the story about Jesus to match a predominant literary hero motif. If that is correct, the RR reference class has no effect. You can disagree but, well, that’s for another time. My point would be that on this view, it is very difficult to reason why the prior chance Jesus existed should be just 6%.
So there is no way to avoid the effect of his being in the RR class by trying to call attention to his being in the “people a human lifespan later believed Jesus was historical” class. You have no data for that class anyway. You certainly have no data for the effect of being in both classes (both a Right Wing Libertarian and in Idaho).
Well, as noted before I don’t need data for both classes any more than you do but at any rate, I would argue we have such data for nearly all historical characters who was thought to have been historical within a lifespan… so that reference class would suggest historicity. I agree we still need to account for the RR data, but the crux is that this cuts both ways: You also need to account for the “thought to be historical within a human lifespan”-data.
The bottom line is, I am actually deriving my epistemic prior from all the data that’s in b. You want to invent non-existent data for mere possibilities and somehow alter the outcome…from whatever your imagination invents as the required data. I’m using actual data. You are inventing data. That’s the difference between us. And on that difference, only one of us is being reasonable.
I think it is quite apparent that you are deriving the reference class using only the RR hero counts and thereby the background information is being reduced to only the RR hero criteria. I am not “inventing” any new data, I am pointing out that existing data in our background knowledge (like the timing of the belief Jesus was historical and the way the Gospels were composed) should be considered relevant — again that’s just how I understand the quote of Dr. Rank.
I understand you feel that what you are doing is more like “using actual data” because you are counting members of a well-defined set, but probabilities relate to states of knowledge and we got no reason to think they should be well-approximated by such counts.
Your wall of words is just more ignoring of everything I’m saying.
Show me your data.
What set of persons do you draw a prior from. Identify the actual persons. The actual set. The actual data.
And if that set excludes RR heroes, explain:
Why is it valid to treat Jesus as belonging to a set that excludes RR heroes, when Jesus is, by your own admission, in the set of RR heroes?
Hi again,
Well, I think we have made progress as far as getting to the bottom of our disagreement.
What set of persons do you draw a prior from. Identify the actual persons. The actual set. The actual data.
Wait a moment, do you think that the prior probability should be drawn from a set of people like the Rank-Raglan prior? That this is a requirement for a prior?(!)
And if that set excludes RR heroes, explain:
I don’t think there is such a set! Estimating priors by counting members of reference classes is at best only an approximation; that’s why I keep asking for references :-).
Why is it valid to treat Jesus as belonging to a set that excludes RR heroes, when Jesus is, by your own admission, in the set of RR heroes?
The two sets — the RR heroes set and the “lived in recent memory” set — are just sets that we construct by selecting different elements of the background information. Once more, just take a moment to consider your argument could be run in reverse: I could answer:
“Why is it valid to treat Jesus as belonging to a set that excludes “people who lived in recent memory” when Jesus is, by your own admissing, in the set of people who lived in the set of people who lived in recent memory?
The entire point of the reference-class problem is to point out in real-world cases we can select a gazillion different sets that sometimes overlap and often not and that’s a huge mess because they would suggest different prior probabilities. That’s why it is called the reference-class problem!
The prior should be based on actual data.
What is your data.
Sorry for interjecting in what is clearly an old debate, and I am not a patron, nor can I afford to be, but what the learned math professor is saying is that your method of using data to constrain priors, and choosing reference classes with sufficient data to get a reasonable handle on the prior seems to be a new idea in practical Bayesianism. It actually solves a very old and very thorny mathematical problem, namely that there is no rigorous way to assign reference classes a-priori in an unambiguous way so as to derive unambiguous priors. By being ignorant of the problem, you’ve solved it completely and persuasively, and that’s quite an achievement.
Your way involves only using classes where there is enough actual real-world data to estimate the probability, not classes so specific so that there are only a teeny-tiny number of examples, or perhaps only one. In this way, you are constraining the prior probability using real-world data, and so, because the real world is not inconsistent, you are never realistically going to get the vastly inconsistent probabilities that plague normal Bayesianism when it is done using arbitrary purely mathematical criteria divorced from real-world data. The different reference-class assignments will end up consistent (up to controllable and estimable statistical fluctuations) because all the probabilities are real-world derived, not pulled out of a hat,
This is the new idea in Proving History, which I must confess I read, but did not understand. It looked like a very tedious review of Bayesianism. But after seeing this discussion, your idea of only using historical references classes where there are unambiguous real-world measurable frequency estimates for the probability is actually ingenious and very simple, and I think it is new.
This is a major improvement to the use of priors in Bayesianism. Your “Rank Raglan Hero” class is sufficiently broad to get data. The class of “people mythologized within 50 years” is almost broad enough to get data, “Ned Ludd”, “Betty Crocker”, etc. The class of Rank-Raglan heroes mythologized within 50 years consists of Jesus alone, and so is useless.
It would be good to emphasize this point to mathematicians in the future, I think, because this is a really beautiful way to sidestep the ambiguities of ordinary non-scientific Bayesianism (i.e. Bayesian history), and honestly, I never thought of it, and I don’t think any mathematician ever would eiither, because it is easy to “mathematically prove” you can get any answer you want using different crazy references classes, but this involves choosing many crazy classes, which, when you use your method, would obviously necessarily need to leave the classes for which you have sufficient real-world data, and this is your whole point. If you stick to classes where you have data, you don’t get inconsistent results (at least, not more inconsistent than the data’s smallness implies)
Thank you for all your wonderful work, and it’s actually quite amazing that you’re surprisingly and brilliantly right, while the trained mathematician is wrong. I don’t think I need to tell you that this hardly ever happens in math vs. humanities.
I just wanted to get this off my chest, because it really resolves the issue of priors for me in Bayesianism, and nothing I ever read in Bayesian literature ever did. It’s like a hybrid frequentist/Bayesian synthesis. Thanks for that, you’re really making Bayesianism a standardized tool for all real-world thinking, and that’s fantastic.
I’ve seen this a lot in applications of Bayes, so I’m not sure what is novel about it. It’s just what Bayesians always do when selecting reference classes. They usually don’t have to discuss the particular details I do because they usually already have very large classes to choose from; and historians are faced with the peculiar problem of small classes, and thus wider margins of error than other fields allow. But regardless, formally, any reference class you reject in place of another, will still affect the posterior by being introduced as evidence (since e and b must sum to all known facts; so anything left out of b, is in e), if the rejected class has any significant effect (since a 50/50 likelihood ratio will have no effect on a 50/50 prior) and remains large enough (otherwise, any effect it can have, will be too small to even be visible at the resolution we are working with—which realistically, in history, is never sharper than a single percentile). I show exactly how this happens in Chapter 6 of OHJ.
And that’s pretty standard in Bayesian reasoning. Follow the bibliography here and the discussions of reference classing by various authors of treatises on Bayesian logic (list here). My solution really is just a specialized application of Franklin’s. Also relevant is McKenzie & Soll. Basically, it’s just always the case that classes with two few members are inadequately informative, while classes to which it is hard to be a member merely by accident entail the most robust correlations (or else give correlations that make no difference, e.g. correlating eye color to market value of a house one owns will have no appreciable effect and thus can be safely ignored, i.e. a prior to which such a correlation is applied as a likelihood ratio, will update to a posterior insignificantly different from the prior, so the class “houses owned by blue eyed people” can be reliably ignored…a problem already solved in standard statistics; no special Bayesian solution is needed).
But you are right that objective Bayesians haven’t, so far as I have found, made clear that they are indeed unifying Bayesianism and Frequentism, by reducing Bayesian belief measures to frequencies of being wrong given a particular quality of evidence. I think because the debate between them is on another matter that really is a distraction from getting to that more fundamental point. But the reduction of Subjective Bayesianism to Epistemic Frequentism through Objective Bayesianism is a separate issue from how one solves the reference class problem.
Hi Richard,
You wrote:
The prior should be based on actual data.
What is your data.
I am concerned that you might have a very different interpretation of what data is in this context. As you wrote:
What set of persons do you draw a prior from. Identify the actual persons. The actual set. The actual data
If you mean that data has to be a set of people from which we can compute a frequency (as the above quote requests) my answer is simply that this is not what ‘data’ means in a Bayesian context: What we have is background information, containing for instance the RR information and the church history, but this information (taken together) does not correspond to any finite set of historical characters we can compute a probability from as you have pointed out. The definition of “data” implied by this description is that corresponding to finite frequentism which (as we agree) is not the same as a Bayesian view of probabilities.
If this is misunderstanding your quote can you please clarify what you mean by data and (again) try to clarify how you use reference classes with a reference to the literature?
To answer your question, the “data” is all of the background knowledge, including (say) that Jesus according to church history and the Gospels was known to have lived (relatively) recently. You can disagree that this has any relevancy, but I would again point to the quote by Dr. Rank, that the RR criteria only informs us that people choose to tell the story about Jesus in a certain way and “Accordingly, if the life of Jesus conforms in any way with the standard hero pattern, this proves nothing one way or the other with respect to the historicity of Jesus”.
So, where do you get your frequency of persons like Jesus typically being historical? What set of persons? And why that set?
I’m going to keep asking that question until you answer it.
Because it’s the only relevant question here.
“So, where do you get your frequency of persons like Jesus typically being historical? What set of persons? And why that set?
I’m going to keep asking that question until you answer it.”
Okay, I appreciate you try to boil this down to a single question so let me
try to summarize my above comments to a single answer so we can move on:
I don’t think there is such a set. I don’t think it is possible to define a reference class consisting of a set of historical/litterary characters such that we can set:
P(h|b) = (#Members of the set who are historical +1) / (#Members of the set + 2)
I don’t think this is possible simply because I don’t think there is anything in Bayesianism that suggests such a set should exist.
Now that I have answered your question perhaps you will take time to answer mine?: Do you believe such a set has to exist and if so, can you provide a reference to the literature on Bayesian statistics to support this view?
You are saying you have no data.
That means we have to use the data we have.
I have data.
So we should start with what we know: and what we know is that RR heroes tend to be ahistorical.
That’s the end of this.
You can’t argue that “RR heroes tend to be historical when they are generated early” if you don’t have any observed instances of that being the case.
You are making things up.
I’m sticking to known facts.
When you give me some facts, I will plug them in and see how it changes the result.
But until you have facts, you are just blowing wind up my ass.
Hi,
In the interest of moving the discussion along, since I answered your previous questions regarding what “set of persons” we should use to compute the “frequency of persons like Jesus typically being historical” (If you recall, my answer was that on the Bayesian view of probabilities we have any reasons to believe such a set exists or we should compute probabilities from such sets), I hope you would answer mine:
Do you believe we should compute the prior probability from such a finite set of historical persons and is that why you ask me to provide such a set? If so, what is your reference to the literature on Bayesian statistics which support or promote this view?
Regarding your new question: “You are saying you have no data”
I am not saying we have no data, I answered that question above:
To answer your question, the “data” is all of the background knowledge, including (say) that Jesus according to church history and the Gospels was known to have lived (relatively) recently
All probabilities in history (and Bayesian models of historical reasoning) are epistemic probabilities. In other words, they are the probability of being right about the conclusion given what you know at the time (Proving History, index, “epistemic probability”). We aren’t doing abstract math here; we aren’t determining absolute truth here. We are modeling what we can confidently say is true (and how likely it is to be), given what we know. The math simply tells us what necessarily follows from what we know at the time.
You have two options (as I demonstrated in Proving History, pp. 110-14).
You can declare the prior probability of the historicity of Jesus to be completely unknown or unknowable, whereby the prior being 0% is as likely as it being 100% or any other percentage. But that entails by mathematical necessity that the posterior probability, the probability you must then assert that Jesus existed, is also as likely to be 0% as 100% or any other percentage (I hardly need show you how the math entails this). This entails that in terms of epistemic conclusions, you are logically necessarily committed to declaring agnosticism about the historicity of Jesus.
Or you can admit you do know at least something about the prior probability of the historicity of Jesus. Which knowledge then entails a probability. Even if what you know is that you don’t know whether it is higher than 50% or lower than 50%, you are declaring that so far as you know (hence “given what you know”) it is 50%. Notably, Lataster ran the numbers using that as the prior and still got a result for Jesus as “probably ahistorical” (in Jesus Did Not Exist). But if you claim to know that it is above 50%, you must actually have knowledge that entails that’s the case. Otherwise, it is false that you “know” it is higher. False by the very definition of knowledge.
And no knowledge exists but on the back of data. All knowledge is an aggregate result of data. Knowledge is composed of nothing else. And therefore cannot exist without it. No data, no knowledge. This is a universal truth of all plausible epistemologies ever devised.
So you have to choose. You can choose to say we have no knowledge whatever about the prior for historicity, in which case you must admit we have no knowledge whatever about the posterior for historicity, and therefore we have no knowledge whatever that Jesus existed. You are then committed to agreeing no one can assert that Jesus existed, not even probably. Or you can choose to say we know something about the prior, in which case you must identify the data that that knowledge consists of.
You cannot escape this.
You want to simultaneously insist we have no knowledge (which contradictorily commits you to agreeing with me that no one should assert Jesus existed any longer, because no one knows he did) and that we have knowledge. That’s self-contradictory already. But even when you pick the second mole for me to whack, and settle on insisting we have knowledge, you refuse repeatedly to tell me what data that knowledge consists of. In other words, you have never justified your assertion of any knowledge in this matter. You just claim to “have knowledge,” but when asked to present the evidence that that knowledge consists of, you refuse to present it, and engage in the fallacy of answering a question with a question, again and again. Thus never answering the question. Which is dodgy behavior at fucking best.
To know that the prior probability of historicity is different for Jesus than any other member of the RR class, you need data showing that it is different for Jesus than any other member of the RR class. If you have none, you have no knowledge on which to assert it’s different. And since the probabilities in Bayes’ Theorem are always what they are given what we know, what we are left with is the prior probability that Jesus existed given what we know. And all we know is that he is in the RR class. Nothing else we know about him tells us anything different about the prior probability of his existing (and you can’t appeal to sets of non-RR heroes to do that, because Jesus isn’t in those sets).
For example, you want to insist “early-made RR heroes are more often historical than other RR heroes” (and it doesn’t matter if you want to run a whack-a-mole fallacy on me and change what proposition you insist; the same analysis falls for anything you choose). But you have exactly zero data to base that assertion on. You do not know that it is true that “early-made RR heroes are more often historical than other RR heroes.” And what you don’t know, can’t affect the probabilities. Epistemically, all we know is that the rate is the same. We could “possibly” be wrong, but possibility is not knowledge of probability (Axiom 5, Proving History, pp. 26-29). When we don’t know, we don’t know. End of story (see analogies in Proving History, pp. 229-56).
You might try to argue that the rate “must” be different, because such rapid mythification is less probable than long durée mythification. But I already refute that in OHJ (“Rapid Legendary Development,” pp. 248-52). Not only do we know many cases of exactly that happening, in even less agreeable conditions, thus by cases already refuting a presumption of its improbability (Ned Ludd, the Cargo Cult saviors, and Roswell: OHJ, index, sic), but even more mythification necessarily occurred by the time even of Mark’s writing (missing sun, mass pig murders, triumphal entries, fig tree witherings, etc.), thus refuting any notion that persons could not be as made up in it as purportedly mass-witnessed events. As I say in that section, “in fact, it’s actually far easier to invent stories about a non-existent person than about one who recently lived,” because there won’t be witnesses to gainsay you, that anyone can plausibly locate (OHJ, p. 150). So the improbability of rapidly selling Jesus as an RR hero is greater if he existed than if he didn’t. Yet there is no dispute that they sold Jesus as an RR hero from the very first time any history was written of it. So it cannot be argued that their inventing him is improbable. It can’t be any more improbable for him than anyone else in the RR set.
And you have exactly zero evidence to the contrary.
So you cannot assert a different prior for Jesus than for other members of the RR set. Until you have evidence that some members of the RR set have different priors than others. (On account of any detail you want; but you still need evidence that that detail makes that difference; and you have none).
Hi,
Thank you for your response. Since it is quite long I will just limit myself to the most important things. The good news is that I feel we are getting to a kind of common understanding unless I am misunderstanding what you understand by “data”.
Firstly, I still agree with you all probabilities in history are epistemic, i.e. conditional on background information :-). I also still agree with you that the math only tells us the consequence of other assumptions :-). So far so good.
As an aside, regarding this comment:
You have two options (..) You can declare the prior probability of the historicity of Jesus to be completely unknown or unknowable, whereby the prior being 0% is as likely as it being 100% or any other percentage. But that entails by mathematical necessity that the posterior probability, the probability you must then assert that Jesus existed, is also as likely to be 0% as 100% or any other percentage (I hardly need show you how the math entails this)
I would invite you to show me the math because I think it is false 🙂 (it is in fact quite similar to what I do in the first part of my review and how the 1 and 2 arise in Laplaces rule of succession which you use if you are interested). Nevermind that’s not very relevant:
Or you can choose to say we know something about the prior, in which case you must identify the data that that knowledge consists of.
This is the relevant case: I think we do know something about the prior. We also know what our data consist of (roughly at least), namely (say) the church history and the RR criteria according to your definitions. If you have a different definition of “data” than what enters the right-hand side of a conditional probability P(X|Y) please let me know (I ask you about these definitions because I am worried we might not be using the same terminology).
I don’t understand/agree with this comment:
You want to simultaneously insist we have no knowledge (which contradictorily commits you to agreeing with me that no one should assert Jesus existed any longer, because no one knows he did) and that we have knowledge. That’s self-contradictory already. But even when you pick the second mole for me to whack, and settle on insisting we have knowledge, you refuse repeatedly to tell me what data that knowledge consists of.
I have repeatedly said I think we have data (background knowledge, i.e. RR criteria, church history, etc.). Can we please agree that I have actually said that repeatedly and move on? I feel you are insisting I am saying something I quite clearly have never said and repeatedly deny.
To know that the prior probability of historicity is different for Jesus than any other member of the RR class, you need data showing that it is different for Jesus than any other member of the RR class.
But this is easy: The church history does not match the other RR heroes, the timing of the gospel source does not match the other RR heroes, etc. etc.
You are free to say: But I don’t think that is relevant. I don’t think it matters that we have (say) the church history for Jesus and something else for Osiris. That’s perfectly legitimate: For instance, if we wanted to compute the chance you got a cold tomorrow, it would be irrelevant your name was Richard Carrier.
My point is to say that I do think it is relevant, and more importantly, to point out that if someone else who was more competent in history felt it was relevant, that we knew something about Jesus that made him (relevantly) different than say Moses, then he would be perfectly allowed to make that judgement and not use the prior obtained by counting Rank-Raglan heroes. As I read your last comments you agree on this point, but just disagree that Jesus is relevantly different.
You can point to your authority at this point and say you have a PhD in history and therefore your opinion should weight stronger than mine in terms of determining what’s relevant; that’s perfectly fine (but can we then please then get over this tiresome pointing out I am supposedly incompetent at statistics in the absence of better evidence?), my purpose of examining OHJ was never to get into whether the ratio of two probabilities should be 1.05 or 1.1. While I think these probabilities might exist out there theoretically, I often feel assigning them numerical values is a bit like when R2D2 computed the chance of Luke Skywalker surviving being eaten by the sandworm in Star Wars 6: How on earth could he know that? This is perhaps a consequence of us having very different expectations of what you need to show in order to say a probability takes some value.
Now that I think I have answered your post, perhaps you can answer the question that I have put forward in various forms about 6 times: Do you think that we have to compute the prior p(h|b) using a frequency-based approximation? That is, that this prior has to be computed by defining an appropriate set of historical characters and computing:
p(h|b) = (#Members of set who are historical + 1) / (#Members of the set + 2)
(quite obviously I think this is false).
I suppose if you treat this as entailing a prior probability of 0.50, upon which likelihood ratios can then work, then you are simply assuming knowledge as to the prior.
Since you affirm that’s what you are doing, I’ll assume that’s what you mean and stick with that.
(Since you aren’t affirming radical agnosticism as to priors.)
As I’ve explained repeatedly, we also have the equivalent “church history” for all the other RR heroes placing them in history. So our having that has no effect on differentiating the probability of any randomly selected RR hero being historical.
Attempts to claim we have something different (e.g. “early church history”) I’ve already refuted: either we don’t have that, or we have no data showing that having it has any effect on differentiating the probability of any randomly selected RR hero being historical.
You are inventing a difference. You have no data showing any such difference would obtain. You just “assume” it, by declarative fiat. That’s not data. That’s making shit up.
I showed you the actual pertinent data (it’s all covered in the “Rapid Legendary Development” section of the book, including the rapid invention of historical facts more grandiose than a mere man, and including the Roswell data, to which I have noted you must add the Frum/Navy/Ludd data, covered elsewhere as background knowledge in the book; likewise the data about lifespans and document access).
You have shown me exactly nothing in return.
You want there to be a difference in expectancy created by the chronology. But you have no evidence showing that there would be any such difference. Whereas I’ve shown you plenty of evidence that there wouldn’t be a difference.
So either you accept the only evidence presented in this debate (mine), which refutes you. Or you admit there is no evidence bearing on the matter that can be cited. In which case, no evidence = no knowledge, no knowledge = no grounds for saying we know the prior to be different for Jesus than for any other member of the RR set.
That I have had to explain this to you half a dozen times now shocks me.
Your question doesn’t even make sense. As opposed to what?
Remember, all other approximations, reduce to an estimation of some sort of frequency, even if not the one you think (Proving History, pp. 265-80).
So what are you even asking?
If we know what the base rate of ahistoricity/syphilis is for a population group (and in this case we do), why would you ignore that data when estimating the prior for the same test applied to a new subject?
The question, then, about whether we “need” to use such a method is completely moot. When we have the data, we cannot ignore it. If we know the base rate, that’s the base rate. End of story. You can’t then not apply it. It’s in b. It has its effect. No matter how much you might want to try and wriggle out of that unavoidable consequence.
This is again demonstrated in Chapter 6 of OHJ, where I show you can assign any prior you want, based on any wild reasoning you want, and then treat the RR data as e and run the equation, and get a posterior that you then apply as the prior when entering further evidence. And still you get the same result.
So your attempt to deny we have data establishing a base rate looks disturbingly desperate. Using excuses like “we can derive base rates differently” is a waste of time, when doing that requires ignoring the data we actually have. Ignoring data = invalid result.
So far as we know, picking any RR hero randomly out of a hat gets us a historical person no more than 1 in 3 times; and Jesus is in that hat. Everything else is not knowledge but speculation. As I’ve explained. Again. And again. And again. And again. Until you give me evidence and not speculation that the rate will be different for Jesus, you do not know that it is. Whereas we do know that for all RR heroes, it is what we observe it to be. If you have evidence it’s different, present it. Otherwise, wind up my ass is all you have here.
Hi again,
I have been a bit way for holiday and have not had a chance to read your response.
Just to clarify something, regarding this statement:
I suppose if you treat this as entailing a prior probability of 0.50, upon which likelihood ratios can then work, then you are simply assuming knowledge as to the prior.
Since you affirm that’s what you are doing, I’ll assume that’s what you mean and stick with that.
No, I simply made my comment in reference to this statement of yours in the previous quote:
You can declare the prior probability of the historicity of Jesus to be completely unknown or unknowable, whereby the prior being 0% is as likely as it being 100% or any other percentage. But that entails by mathematical necessity that the posterior probability, the probability you must then assert that Jesus existed, is also as likely to be 0% as 100% or any other percentage (I hardly need show you how the math entails this).
that is, the situation you outline above where the prior probability of historicity itself is treated as an unknown parameter which is as likely 0% as 100% as you wrote. I would still very much like to see your math on that situation you had in mind with that quote since I don’t think I agree with your conclusion.
At any rate, I think we have finally laid bare the source of our disagreement. For instance you write:
As I’ve explained repeatedly, we also have the equivalent “church history” for all the other RR heroes placing them in history. So our having that has no effect on differentiating the probability of any randomly selected RR hero being historical.
Yes, I agree we have the equivalent of a church history for Moses, Jesus and Hercules, but they are different. What your computation for the prior assumes (if seen in the standard Bernouilli/beta) setting) is that the probability of the heroes being historical given their background information are all the same. The issue is that I simply don’t think it is true since they have different histories. I.e. if we consider the “church history” for Moses this would be centuries after Moses having supposedly lived whereas for Jesus it is much sooner after his supposed life. I think when we consider Jesus (vs. Hercules) and the earliest documented groups who wrote about these characters it is self-evident that they are treated differently and in a manner which can’t be ignored if we consider their historicity. You might simply disagree with me on this point, however my purpose of the review is to try to make readers aware that this type of assumption underlies the Rank-Raglan prior and a reader can then make up his mind if that is reasonable: If he feel it is, he should agree with you, if not, he should feel free to come to some other conclusion regarding the prior probability of your 5-point myth theory.
You are inventing a difference. You have no data showing any such difference would obtain. You just “assume” it, by declarative fiat. That’s not data. That’s making shit up.
I don’t think that is a fair assessment of the situation. You still have not defined what “data” means in this context, however since all terms that enter the Bayesian computation is our assessment of subjective degrees of belief I don’t see how “data” could mean much else asides a recognition of different background information for Jesus and the other Rank-Raglan heroes (objectively a true statement; they do have different church history) and a (subjective) assessment that this difference matters. That assessment can be more or less informed, I agree, but as all terms in your computation it is still only that: An assessment of what is a reasonable probability based on a consideration of available information.
I would like to ask you in return since I believe you also carry a burden of proof: What is your data to show Moses and Jesus are similar despite their different “church histories” (and other particular background information)?
I showed you the actual pertinent data (it’s all covered in the “Rapid Legendary Development” section of the book, including the rapid invention of historical facts more grandiose than a mere man, and including the Roswell data, to which I have noted you must add the Frum/Navy/Ludd data, covered elsewhere as background knowledge in the book; likewise the data about lifespans and document access).
I agree myths can develop fairly rapidly, however there is an important piece of information to be taken into account: John Frum is only partly analogous to Jesus since John Frum did not start in the supernatural realm and was then transformed onto earth later by communities that came to believe the supernatural stories are real. John Frum therefore matches part of your Jesus case (rapidly being placed in history) but not others. It is akin to using a person who plays the saxophone but does not like skiing to argue in favor of a large prior for people who play saxophone and like skiing.
Regarding my question “Do you think that we have to compute the prior p(h|b) using a frequency-based approximation?” you wrote:
Your question doesn’t even make sense. As opposed to what?
Remember, all other approximations, reduce to an estimation of some sort of frequency, even if not the one you think (Proving History, pp. 265-80).
So what are you even asking?
If we know what the base rate of ahistoricity/syphilis is for a population group (and in this case we do), why would you ignore that data when estimating the prior for the same test applied to a new subject?
I thought my question was fairly simply, but let me rephrase it: Do you believe the prior for ahistoricity has to be computed by finding an appropriate, specific set of characters known from literature and approximate:
p(h|b) = (#Members of the set who are historical + 1) / (#Members of the set + 2) ?
This is again demonstrated in Chapter 6 of OHJ, where I show you can assign any prior you want, based on any wild reasoning you want, and then treat the RR data as e and run the equation, and get a posterior that you then apply as the prior when entering further evidence. And still you get the same result.
I agree (as I write in my review) that if probabilities are selected appropriately this is true. But I would very much like to see a non post-hoc treatment of the rank-raglan information that lead to that result. It will assume a reading of the Gospels where we dismiss all the times Jesus interact with historical characters and do things most people do as irrelevant to history, but then when he does something commensurable with the Rank-Raglan information we assign that large historical relevancy in terms of Jesus historicity. That simply does not strike me as something I would be comfortable doing, but I would very much like to see you run this argument if you like.
So far as we know, picking any RR hero randomly out of a hat gets us a historical person no more than 1 in 3 times; and Jesus is in that hat.
Well, I think the difficulties with this type of “he is in the hat”-kind of arguments should be self-evident: Picking a random person out of the hat of “all men” gets you the president of United states about 1 in a billion times and Obama is in that hat; this should not convince us that we should ignore additional information we have about Obama, or that Obama belongs to many “hats” defined by different sets of information (see earlier remarks).
Fallacy of Reversed Responsibility (see here and here). The burden is on you to show that that difference affects the frequency. No evidence it does, no reason to conclude it does. No data, no knowledge.
You could just as easily say that one’s name starts with J and the other M, and that this makes them different, and therefore the frequency must differ. That’s more absurd, but the same fallacy all the same. Because the evidence does not show the timeframe you are talking about has the effect you claim (Ludd, Frum, Navy, Roswell, and the contents of the Gospels themselves, e.g. erased sun, triumphal entry, mass child and pig murders, mass resurrections witnessed by all Jerusalem, etc.).
Show it has the effect you claim. Until then, you cannot claim to know it has that effect. Or any.
Fallacy of Reversed Responsibility (see here and here). The burden is on you to show that that difference affects the frequency. No evidence it does, no reason to conclude it does. No data, no knowledge.
That’s interesting. When I consider the historical context (church history) surrounding (e.g.) Zeus it seems to me that it is obviously radically different both in terms of what people believed early on about Zeus (another God in the Pantheon vs. a miracle-worker) and when that it seems obvious to me that the chance Zeus is historical on those grounds alone is significantly lower than Jesus (that is, they can’t be considered to have the same chance of historicity a-priori).
Perhaps you will agree with this assessment of what we are both saying: If a person disagreed with you that the church history (and other background information) of Jesus and Zeus are the same in terms of determining these two characters historicity, then that person would be justified in not accepting your Rank-Raglan based prior?
Regarding the burden of proof: Well, this brings us back to the discussion of what constitute proof when we are both guessing subjective probabilities.
You could just as easily say that one’s name starts with J and the other M, and that this makes them different
But since I did not make that claim that would be a false analogy. A more apt analogy would be something I had actually said, like if we agreed to this whole finite frequentism business we could consider Jesus to be part of the class of people who “were believed to be historical within 50 years of them having supposedly lived”. That class would contain a few mythical people like John Frum, but it would also contain you and I and many historical characters from the ancient world. Blow by blow the discussion could proceed as follows:
(1) You could say that this class was falsely equating Jesus with people who were very different than him (like I point out Jesus is different than Zeus in various ways)
(2) then I could ask you “what data and knowledge” you had to prove that was the case (like you ask me what data I have to prove Hercules is relevantly different than Jesus)
(3) you could then say that you simply felt the difference between the prior chance of Jesus and I being historical was different on the face of it because we are so different in many relevant ways (like I am claiming the church history and other difference in the historical setting of Zeus (described as a member of a pantheon of Gods) and Jesus is obvious)
(4) Then I could say that you had to produce “data” to demonstrate that was the case (like you are asking me to produce data)
(5) Then you could ask me what “data” supposedly means since we seem to be discussing my view of what is allowed to constitute relevant differences and if I have any citations to the litterature to demonstrate this as a valid way of obtaining prior probabilities (like I have asked you to define data many times)
(6) I could ignore that question and repeat: Jesus DOES belong to the class of people who was thought to have been historical 50 years after them having supposedly lived. we have DATA to demonstrate this (The Gospel of Mark). You have NO data. (like you have ignored many similar questions of mine about what constitute data and repeated that Jesus belongs to the class of RR heroes and asked me for “data”)
They are no more radically different from each other than they all are from each other, by your standards of what counts as “radical.” Differences do not matter until you can show they do. You have not shown they do. If you disagree, show the evidence that warrants your disagreement (not just that “there are differences,” but that they alter the frequency, and what they alter it to). Otherwise your disagreement is with reality. And obviously I can’t convince anyone of anything who insists on disagreeing with reality.
Hi,
Before we discuss the specific, historical questions perhaps it would be a good idea to just get a clear view of your position.
Just to be clear: Your contention is that the probability Jesus and Zeus are historical given our background information (i.e. information such as the church history of Jesus and the equivalent for Zeus) is the same?
And as a followup, if a person did not agree with you regarding the above question, you agree that he would have to replace the RR prior with something else?
My contention is that the prior probability of the historicity of every member of the RR set is the same; therefore the prior probability is the same for Jesus and for Zeus. Were the RR set not that indicative, we should have found many historical persons in it. That we didn’t, entails being in it is strongly predictive of ahistoricity. Evidence can reverse that conclusion, e.g. if Paul clearly referenced Jesus as a recent historical figure on earth (e.g. mentioned that Peter traveled with him) that evidence would be so improbable on ahistoricity it would overwhelm the prior probability resulting from Jesus being an RR hero, and establish a high posterior probability that Jesus existed.
Until we present such evidence, we can’t conclude otherwise. And this is true even if we put the RR data into e and start with a neutral prior (of 0.5) and run the equation just for the RR data, which would give us a posterior the same as the prior I use, which would then become the prior in the next run of the equation, when we add in all the other evidence in e. There is no data that we could run that has any different effect, because we have no data pertaining to RR heroes that shows any different effect (and classes that don’t contain Jesus don’t apply to Jesus, and classes that don’t contain RR heroes don’t apply to Jesus, who is an RR hero). Even hypothetical sets based on analogous precedents don’t give us any usable changes in frequency (e.g. “savior gods/founder heroes” like Ludd and Frum; paranormal legends like Roswell; etc.), being either the same, indeterminate, or too variable for an effect to be visible. We do not know that any of the ways Jesus is different from Zeus make the historicity of Jesus more likely (beyond too trivially to show in the math at the rounding level I employ).
Anyone who does not agree with this, does not agree with reality.
Pardon the intrusion,
It seems like what Tim Hendrix wants to do is create a new reference class which contains only Jesus (RR + church history). Now, this requires demonstrating somehow that the church history is different from all other RR heroes, which seems hard, especially since our background knowledge also includes the fact that Christianity had a monopoly on the preservation of recorded information, so our knowledge of church history is simply better than other RR hero cults. But let’s just allow him that assumption – Jesus belongs to a unique class {RR + church history}.
That actually conveys zero prior information, because we want to ask about whether or not Jesus existed. So at best the prior is 0.5. (Because 1/(1+1) = 1/2). Basically, a reference class that includes only one member is like saying we have no background information that matters.
It’s also worth noting that this effectively excludes all the RR information from b (because all the features of being an RR are effectively ignored, by declaring him a unique exception to it), so it must be incorporated into e, which means the clearly legendary nature of the gospels becomes evidence against an historical Jesus. (If it’s not in the background, it must be included in the evidence). In short, the unlikeliness of being a RR hero still affects the posterior probability, we’ve just forced it into e instead of b.
Consider the Right Wing Libertarian (RWL) from Idaho. If there were no other RWL from Idaho, then by restricting your reference class to ‘from idaho’ would mean there are no parallels to draw with any other class members. By making a unique class member, you’ve excluded all known correlations between RWLs from the background. Which means you’d have to consider those things under evidence (because you can’t exclude knowledge), and they’d still have to be overcome by specific knowledge against them that we have for our RWL from Idaho. (ie, surely the fact that he’s a RWL has some bearing on his beliefs, otherwise he wouldn’t be a RWL at all. And when he disagrees on particular points, that would need to be demonstrated with specific facts pertaining to our unique RWL from Idaho that override the general RWL correlations).
I’d also note that the church history that Tim Hendrix wants to incorporate into b is already in e in OHJ. ie, this evidence was not ignored. It doesn’t matter if it’s in b or e, so long as it’s factored in.
Which is really the take home message here: as long as it factors as evidence somewhere, it really doesn’t matter if you put it in b or e, and quibbling about where you do so is just that, quibbling, and not a debate of real value.
Yup.
I thought Hendrix’s most trenchant point was in the “addendum” of his paper, p.43, where he pointed out that Carrier made an assumption of independence where it is unwarranted. I haven’t been able to find Carrier’s defense of this assumption. Can he comment?
In OHJ I am using dependent probabilities in every section (one can tell by the paragraph wording establishing each estimate what dependent variables are affecting the assessment). There is no assumption of independence in OHJ anywhere he claims. It doesn’t exist. So that’s just another example of Hendrix not actually reading the book.
You might notice he never cites any example or page number attesting to what he is talking about anyway. He only mentions something vaguely about my assignment for 1 Clement, and nothing else; but he gives no page number or quotation regarding my estimates on that, nor explains how my estimates are not dependent probabilities.
I suspect Hendrix is making similar mistakes to Kamil Gregor, ignoring the role of my error margins and the actual basis I state for each probability. But since Hendrix never explains what in OHJ he is talking about or how he is deriving anything he claims from it, it’s impossible to ascertain where he has gone wrong.
No, I’m referring to way you combine the probabilities of individual data points. For example, on the last page of chapter 9 you summarize 3 data points, let’s say
f1 = “vanishing family”
f2 = “omission of Paul’s trials”
f3 = “remainder of Acts”.
In the course of the chapter you have arrived at your values for each of P( fi | b), i=1,2,3. Then you get
P( f1.f2.f3 | b ) = P(f1|b)P(f2|b)P(f3|b).
But this is only valid if you assume that the fi|b are independent of one another.
No, that’s incorrect. They can be dependent probabilities. And in every case you mention (which are not mentioned in Hendrix in this respect), they are. Perhaps you don’t know how the math works, but the correct way to multiply probabilities is to recognize their dependency. You do not have to assume their independency. If you don’t understand what I mean, I give another example in A Bayesian Brief on Comments at TAM. But I’ll explain using your example here.
First, note that I find P(f3|h) to be 1 all around, even at both margins of error, so it has no effect at all on P(h|e). This is actually because I am providing a dependent probability: if it is already the case that Jesus existed (or didn’t) and still Luke omits 1 and 2 (or also did), then the remaining contents of Acts have no further effect on P(h). This exemplifies how dependent probability works, and how it impacted my values: my P(f3) is already dependent on f1 and f2, and that’s why P(f1) washes out as 1/1, having no effect.
So I will assume you mean to focus on f1 and f2, the only features I find have any effect on the probability of historicity. I’ll proceed on that assumption.
Given that Jesus didn’t exist, the probability of those two observations (f1 and f2) is high-ish; but if Jesus did exist it is low-ish. But the probability of having only one of them (say, f2) is not as high; likewise, if Jesus existed, not as low. Our math has to account for this, because it’s not the case that, say, P(f2|f1) = 1; after all, Jesus could not have existed and still Luke made up references to his historicity in Paul’s speeches, and Jesus could have existed and somehow those speeches still lacked, or Luke removed (perhaps seeking brevity?), references to the fact. The probability of either is not zero, even given the absence of brothers (which can have its own separate cause—like, the historical Jesus had no brothers), and so it cannot be the case that P(f2|f1) = 1 or that P(f1|f2) = 1. Therefore, when I give a probability for any segregated item in Acts (which is really, only those two), it is the dependent probability; formally, what I present is P(f2|f1.f3.b.h) and P(f1|f2.f3.b.h), against P(f2|f1.f3.b.~h) and P(f1|f2.f3.b.~h). The math then follows, correctly as I calculate. Hence I am already running dependent probabilities. I am not running independent probabilities.
Another way to think of it is this: given that Jesus didn’t exist, we expect f1 and f2 given that Acts contained relevant sections f1* and f2*. For example, if Acts had no speeches of Paul, then we couldn’t say how likely their content would be on h or ~h and thus we’d lose the effect of f2 on the total probability of historicity, which means any negative effect I find it has would wash, and the probability of historicity would go up. The question then is: by how much would it go up? Well, by exactly as much as I assess it goes down—given that we do have f2* and it does have those omissions.
This is how cumulative evidence works. The more evidence in the same text for any hypothesis when that evidence is not strictly entailed by the previous evidence, the higher P(h|e) must go. You can’t claim “as soon as you have any single item of evidence in that text, then your P(e|h) is always fixed at that and never goes up no matter how many other items of evidence we find in that text supporting h.” Obviously, as some items of evidence in the text could be stronger than others. So they can’t all be the same, even individually, much less in sum. And this is because the dependent probabilities can be lower than one. So you have to work out when they are.
For example, it would be invalid to argue P(f1|e) should go up because Jesus had (so Mark says) four brothers and four missing brothers is more improbable than one missing brother. Because the missing of brothers is an all or nothing effect; the probability is therefore the same no matter how many there are supposed to have been. Once you have one brother prominently mentioned in the public history in Acts, P(f1|e) would swing in favor of historicity, the reverse of what I found. But that’s what I found only because (in fact) no brother is mentioned. That the other brothers vanish is then no more likely on either historicity or ~historicity. That’s how dependent probability works. Whereas, once no brother is mentioned, P(secondbrothermissing|allbrothersmissing) = 1, so adding a second brother’s disappearance has no further effect (because any probability multiplied by 1 remains unchanged). That’s also how dependent probability works.
But since Luke could have made-up stories about the brothers of Jesus, their being in the public history of Acts would only increase P(h|e), it would not make it equal to 1. And since Luke could have left them out for other reasons even if Jesus existed, their not being in the public history of Acts would not make P(h|e) equal to 0. So we still have to work out what the differential effect is. We can’t just set it to “1” or “0.”
And this effect is independent enough of whatever Luke decided to do (or had materials to use) for the speeches of Paul, such that P(f2|f1) does not equal 1 and thus, unlike stacking up missing brothers, their cumulative presence does have a differential effect on the probability. It short, it’s still less likely on historicity that Luke would do both, than that he would do only one or the other. So we still have to calculate how much less. The way we do this is with dependent probabilities, exactly as I do.
In colloquial terms, Acts has more oddities in it than it could have had; their cumulative effect must therefore be assessed. It is not simply the case that P(f1|f2) = 1, as if Luke’s omitting the entire family of Jesus from the church’s history logically entailed that he would omit references to a historical Jesus in Paul’s trials. It doesn’t. We thus have a causal question to answer: why did Luke do each of those things? Since his reasons could be different in each case, the probabilities are partially independent, and thus we have to ascertain their actual dependent probability, which is not going to be 1.
Another way to think of it is this: if we want to be able to test these things, we need to tease them out so we can see the effect of removing them on the conclusion. This is, I suspect, what Hendrix does not understand. So, what would P(Acts|h)/P(Acts|~h) be, without f2? That is, keep f1, but have a copy of Acts lacking f2. Obviously, P(Acts|h)/P(Acts|~h) should go up in such a case. Thus, even as a probability dependent on the presence of f2, P(f1|h)/P(f1|~h) still has a different value than P(f1.f2|h)/P(f1.f2|~h). We need to assess what value that is. And that’s what I do.
That’s why my estimates of the impact of this evidence (f1 and f2) are so low: they are taking into account their possible causal conjunction. After all, maybe Luke had separate or the same reasons to do f1 and f2 even though Jesus existed. Whereas if Jesus didn’t exist, then f1 and f2 are fully expected, and thus their dependence is irrelevant, because they are already topped out in probability, and thus have the same value even multiplied together (because 1 x 1 is 1); it’s therefore only their improbability on h that has any effect on the total probability. So then we have to assess whether the conjunction of f1 and f2, given h, is just as likely as f1 or f2 alone, and what I find is no, it is not. The conjunction is still less likely than either alone. Unlike in the case of f3, where I find the conjunction, given the same dependence, is as likely either way and thus has no effect. And all I am doing in OHJ is displaying that fact mathematically.
Slight nitpick: You didn’t “find P(f3|h) to be 1”, you found the ratio P(f3|h)/P(f3|~h) to be 1. But I agree that f3 doesn’t affect the calculation.
“…what I present is P(f2|f1.f3.b.h) … against P(f2|f1.f3.b.~h)…”
So are you saying that in the section of that chapter where you looked at f2, you were assuming f1 and f3?
And in general, in the section of the chapter where you looked at fi, you were assuming the other 2 f’s?
Then you would be calculating
P(f1.f2.f3|b.h)/P(f1.f2.f3|b.~h) =
P(f1|f2.f3.b.~h)/P(f1|f2.f3.b.h) P(f2|f1.f3.b.h)/P(f2|f1.f3.b.~h) P(f3|f1.f2.b.h)/P(f3|f1.f2.b.~h)?
Is that what you did?
I actually did both. After factoring out the common coefficients of contingency (all the random factors that equally affect the outcome on either theory, e.g. the exact stories and words chosen by the author of Acts, which could have varied endlessly but make no difference to what we are measuring: see notes on p. 289, and directly on point, p. 605), P(f3|h) is indeed 1, as is P(f3|~h), i.e. the text (apart from f1 and f2) is 100% as expected on either theory (even given f1 and f2). That is why their ratio is 1 (as it would still be if we left those coefficients of contingency in, since by definition those have an identical value on either side of the ratio).
Yes. And everywhere else in OHJ I break out individual textual evidence from the same author. Including the other way around (e.g. in Ch. 11 on the a fortiori side I assess the evidence of parentage and brothers separately but combine them in the final analysis, so the inclusion of both is stronger evidence for historicity than if we had only one; this is again a dependent probability assumption, since Paul would be the author of both or either).
This should be clear from the wording of the text of those chapters. I nowhere claim these are causally independent of each other. My assessment of their particular odds is always in respect to their own improbability even coming from an author we already assume is inventing history [~h] or recording it [h]. I even have a section in Ch. 9 on what happens if we remove the dependent assumption of any contact with history in Luke (so that he must be inventing regardless of ~h or h); and a section in Ch. 12 on what happens if we do abandon that assumption (pp. 603-04).
Hendrix I noted has a very hard time with colloquial English. I think he doesn’t do well ascertaining the mathematical model of an ordinary sentence in English, and has a tendency to import assumptions as to what is being said in a sentence, that is nowhere being said. Hence, for example, no one has any business assuming an estimate is independent unless it is declared to be. One should always first analyze whether what is being presented is a credible dependent probability because the math requires it to be. Rather than assuming someone is doing something else, you should always first assume that they are doing what they are supposed to be doing. And only if you then find an error can you claim there is one.
Your equation at the end has some mistakes in it, so I can’t answer that specific question, but I think you meant to write:
P(f1.f2.f3|b.h)/P(f1.f2.f3|b.~h) = [P(f1|f2.f3.b.h)/P(f1|f2.f3.b.~h)] x [P(f2|f1.f3.b.h)/P(f2|f1.f3.b.~h)] x [P(f3|f1.f2.b.h)/P(f3|f1.f2.b.~h)]
Which is not correct. Because in a single equation you have to decide where to put each f, whether in e or b; and you can run the equation iteratively, i.e. you’d have a run of equations rather than a single equation like this, where by the end all e ends up in b (since b, like h and ~h, has to have the same content across the equation).
I might have misled you there so let me explain it from a different angle:
Note that here, f3 is a meaningless import (it becomes like “the moon is not made of cheese,” a background fact of no relevance to the outcome), so it really need not be in the equation (any more than “the moon is not made of cheese” should be). It’s here just a placeholder for “there is no other evidence in Acts bearing on the question.” Had that not been the case, f3 would be something else, something specific, and we’d move this f3 to f4, and so on.
So really the only question is, can we evaluate f1 knowing f2 is coming up?
In other words, can we use the method of iteration (p. 240, 509. nn.) and still get the same result—as we should, since order of the presentation of evidence should not affect the outcome in most cases.
In that case, formally we would not have a single equation, but two in succession (the full equation only represents the final end result of all iterations). If it’s the case that we “find” f2 only after we calculated the effect of f1, so that we can’t have conditioned f1 on finding f2, would this change the math? The answer is no. Because the common dependent causes remain the same (h or ~h are the common root cause of both f1 and f2, and h or ~h are already conditional terms when evaluating f1 before we get to f2; likewise b already includes “the entire content of Acts has the same author,” hence both f1 and f2 are already conditioned on that fact as well, and so on). Insofar as f1 and f2 have separate necessary causes besides that, they don’t cross and thus don’t have to be accounted for as common conditions (e.g. on h, possibly “Jesus had no brothers” must be accounted for when evaluating P(f1|b), but it has no effect on P(f2|b); conversely, possibly “Luke unknowingly cut indicative material when he abbreviated Paul’s speeches” must be accounted for when evaluating P(f2|b), but it has no effect on P(f1|b)).
This is what I was explaining with the “number of brothers” counter-example. In that case, there is another common cause: once Luke makes the decision to exclude the family of Jesus regardless of why that is (whether “he had none/they had no historical role then” or “Luke wanted to erase them”; or, “there was no Jesus”), it causes the same outcome for f1, f2, f3, and f4, where these now are individual “missing brothers.” Then, “Jesus had no brothers” must be accounted for when evaluating P(f1|b), and does have an effect, indeed exactly the same effect, on P(f2|b), where “f2” is “second brother” rather than “Paul’s weird speeches.” Thus, we don’t get any further impact on P(h|e) from f2, f3, f4, etc. And that’s why I make no case that they do. The whole fact of missing family exhausts its effect in one go.
By contrast, our actual f2 (Paul’s speeches) is causally distinct from f1 (as in, f2’s presence or absence does not of itself affect the presence or absence of f1, but for their common cause, which is included within h and ~h and of course b, e.g. “the content of Acts has the same author,” which is always what P(f1|b) is conditioned on, requiring no knowledge of f2). That’s why I can treat them separately (and indeed, should). And that’s why an iterated method would get the same result, e.g. P(f1|b.h) will have the same value as P(f1|f2.b.h) once we recognize what’s already in h and b, like “Jesus existed” and “the content of Acts has the same author” and “the author of Acts had historical data of some kind, whether or however he used it” and so on.
To argue against this, one would have to demonstrate somehow that f2 would make f1 more likely on h than I estimate it to be (since it can’t make it more likely on ~h; on ~h it is already pegged out at 1), or somehow that f2 would make f1 less likely on ~h than I estimate it to be. Otherwise anything else would reduce, not increase, the probability of historicity (which is also logically possible, but I am assuming that isn’t a critique Hendrix intends to make, but one could do, i.e. someone could argue I under-estimated the impact of f1 on historicity, because of some overlooked causal relationship from f2, although I don’t see how—if I had, I’d have noted it).
So, Hendrix needs to do that. He can’t just say “Carrier overlooked a causal dependency.” He has to actually identify an actual causal dependency I overlooked. That kind of criticism I’d welcome. But you have to actually do it. You can’t just handwave and claim it “must” have happened “somewhere” even though you can’t find any examples of it happening.
OK, I think we’re getting somewhere. Let me see if I’ve got your argument:
The odds ratio we want is
P(f1.f2|h)/P(f1.f2|~h) =
P(f1|h)/P(f1|~h) P(f2|f1.h)/P(f2|f1.~h).
You use the approximations
P(f2|f1.h) ≈ P(f2|h)
P(f2|f1.~h) ≈ P(f2|~h)
because f1 and f2 are essentially independent (and to the extent that they’re not, the approximation favors h).
Is that correct?
No. Or maybe yes.
f1 = “vanishing family”
f2 = “omission of Paul’s trials”
These are dependent probabilities. Although maybe you are using “essentially independent” in a colloquial way and you simply mean dependent probabilities without full causal determinism (like I think you mean at the end).
So, key point is, that doesn’t change their value.
Maybe you think that their being dependent probabilities somehow entails their probability values should change. By itself that is mathematically false. To see this, just try building any coherent argument for changing either of them. What do you think should change about them and why? Work through it and maybe you’ll get what I mean.
Because dependent probabilities still multiply. Exactly as I have them. There is no change to the math required by any dependency between them. As long as their probability value is correctly calculated on their dependency and not on an assumption of their independence, before multiplying them.
That is why f3 remains 1 on both h and ~h: its probability is dependent on other evidence (e.g. the Gospels). We fully expect Acts to include references to historicity derived from the Gospels (particulary GLuke itself) regardless of whether Jesus existed. What we need is something that is not fully causally expected like that.
There are only two things that are: the missing people (not just the brothers, but e.g. his mother and father) and the strange omissions of a historical ministry or any of its events in Paul’s trial speeches. Is either of those 100% expected given the other? No. Therefore, you have to determine what their dependent probabilities are before multiplying them. And it won’t be 100% on h, for either of them.
That’s what I did.
So all you can do at this point is argue for a different assignment of P to either or both, even by appealing to dependency relations. So, let’s see what your argument for a different value is. Then I can show you why you won’t end up with any meaningfully different result. Or you will convince me they should be altered.
P.S. One way to walk through this is to use iteration. All Bayesian priors are the outputs of inserting prior evidence. So you can run the equation fully as if you “just discovered” f1. Then use the posterior this generated as the prior and run it again for f2, as if you “later” then suddenly discovered that.
Does anything change?
Does having f1 (which now is in b and not e) change P(f2|h) or P(f2|~h), because now it’s P(f2|h.f1) and P(f2|~h.f1)?
Then imagine history went the other way around. Does discovering f2 first and then f1, iterated in the same way, change anything? Or is the end result the same?
If either changes anything, then analyze why (and whether that change is actually warranted). Then we might get somewhere.
So, if you wanted a correct equation for h given Acts alone, it would be (excluding f3 now as irrelevant; it is simply a placeholder for the absence of any other determining evidence):
P(h|f1.f2.b)/P(~h|f1.f2.b) = { [P(f1|b.h)/P(f1|b.~h)] x [P(h|b)/P(~h|b)] } x [P(f2|f1.b.h)/P(f2|f1.b.~h)]
Which will have the same value as:
P(h|f1.f2.b)/P(~h|f1.f2.b) = { [P(f2|b.h)/P(f2|b.~h)] x [P(h|b)/P(~h|b)] } x [P(f1|f2.b.h)/P(f1|f2.b.~h)]
To make a valid critique of this, one has to demonstrate that those would not have the same value. You can’t simply assume that they won’t.
Still thinking about my last comment? I’d really like confirmation that we’re finally on the same page.
I reversed f1 and f2 because that’s the order in which you dealt with them in the book.
I disagree with you here though:
“To make a valid critique of this, one has to demonstrate that those would not have the same value. You can’t simply assume that they won’t.”
If you assume independence, the burden is on you to justify it. I think it can be justified though, as I suggested in my last comment.
As I wrote:
That fully justifies my point.
There is no logically necessary relation between “Jesus existed and Luke omitted mention of his brothers” and “Jesus existed and Luke omitted any mention of that from the trial speeches of Paul.” The order of examination is not relevant (there is no logically necessary relation in the other direction either). Therefore they cannot wash out into a single probability. Their causal dependency is mediated by additional unrelated causes. Thus, you still have to determine the probability of each, when both exist. Yes, you are then calculating dependent probabilities. But dependent probabilities are still distinct probabilities.
So you aren’t making any relevant point here.
Try making a coherent argument that one of those two probabilities should be different than I assign them. Then maybe you will see the problem with what you are claiming.