Why Not a Christian Now an Audio Book! »« Comments & Moderation Policy

McGrath on Proving History

James McGrath has reviewed my book Proving History. We’ve argued before (e.g. over claims Bart Ehrman made), so there is backstory. But his review is unexpectedly kind and praising at points, and he likes the overall project of explaining the underlying logic of history as fundamentally Bayesian and making productive use of that fact. He does conclude with some select criticism, though, and that is what I will respond to here.

General Points of Agreement

His general point he summarizes thus:

I felt like I had already read two very different books. One of them is lucid, focused, methodologically rigorous, and full of powerful insights. The other reads like a case study in what happens when someone ignores their own sound methodological advice in practice when turning their attention to the figure of Jesus, an exercise which has led even some of the brightest minds in history to write some absolute nonsense, and many more to write things that were merely unpersuasive. I have read many other books where the same criticism could be made that I will here make of Carrier: the methodology is brilliant but the application is problematic.

As a generalization, I wholeheartedly agree with him. But do I make the mistakes he alleges? No. And showing why I do not makes for a good teaching example on how to understand and apply formal logic and Bayesian methodology to history (and to Jesus studies in particular). So I’m quite grateful for his thoughtful review.

The first general point McGrath already well understands, which is that even though Bayesian method can be misused or mistakenly applied (as he rightly says, “garbage in, garbage out”) the great value of it is that it makes this easy to detect, demonstrate, and critique (as McGrath says, “Carrier makes a strong case that Bayesian reasoning can help expose when this is taking place”). In other words, Bayesian methodology makes progress more accessible by making bad arguments more visible, and providing an effective way to expose or correct them.

I fully grant this applies to everyone and welcome its use to correct my own errors, in order to revise my conclusions toward what is genuinely more defensible. I discuss this fact several times in the book, as one of the method’s greatest merits. And indeed, a main mission of my next book (On the Historicity of Jesus Christ) will be to start this kind of productive debate, rather than to end it (in the matter of whether we can really know Jesus existed as a real historical man). But alas, McGrath never once actually uses any Bayesian argument in his critique. Thus he abandons the very tool he just agreed we need to deploy.

McGrath also correctly gets my take on mythicism generally. As he says (and I say much more in support of this point than he singles out for example):

If the internet mythicists of today were to take this advice to heart, they might work on trying to actually publish scholarly works in appropriate venues, instead of complaining about their being dismissed in a manner that Carrier rightly says is appropriate when people without relevant expertise try to bypass peer review and scholarly discussion and promote their ideas directly to a public ill prepared to assess them.

Particularly as there really is plenty of crazy coming from mainstream scholars even in mainstream venues (I’ve mentioned my bafflement at Robert Eisenman’s bizarre theories about the origins of Christianity before, for example, and I needn’t mention that pretty much no one in the field buys them, either), so it’s not like mythicism would really be so out of place there (it’s just dogmatically opposed with more fury; theories like Eisenman’s apparently get a pass because at least they still have a historical Jesus in them).

Dennis MacDonald’s theory that Mark is a literary emulation and transvaluation of Homer is among those McGrath might reject (as it’s often considered a radical thesis, though IMO it’s probably substantially correct, even if not in every detail), yet I’m sure even he would extend it intellectual respect, as it was argued through proper channels and methods. That is indeed what mythicists need to do. And I am working on doing that.

But now to the more specific criticism of my applications of Bayesian reasoning to assess the “method of criteria” now employed in the field of Jesus studies.

Ignorance vs. Embarrassment

McGrath starts by confusing ignorance with provisional knowledge:

For instance, the fact that we do not have a complete and comprehensive background against which to determine what would have been embarrassing to early Christians is by Carrier’s own statements irrelevant, since a Bayesian approach assesses probability based on the evidence we have. If new evidence comes to light, we change our analysis if necessary, but we ought to proceed based on the evidence we have, as Carrier acknowledged elsewhere in the book.

This confuses two different principles, not knowing something and believing we know something (when we happen, unbeknownst to us, to be wrong), which I tease out in Chapter 2 with examples about Julius Caesar shaving or having an imperial moonbase (among other things: pp. 26-29), discussing Axiom 5, “any argument relying on the inference ‘possibly, therefore probably’ is fallacious.” Related is also Axiom 3, “overconfidence is fallacious; admitting ignorance or uncertainty is not” (p. 23). And I discuss this specific problem for Jesus and the origins of Christianity extensively under “The Problem of Ignorance” on pp, 129-34 (and there citing other scholars in agreement with me), and it’s a principle even Bart Ehrman himself affirms (while simultaneously ignoring his own advice).

Ignorance cannot be replaced with assertions of knowledge. If we do not know what was embarrassing to all first century Christians, we do not know what was embarrassing to all first century Christians. Full stop. Anything further violates Axioms 3 and 5. Sometimes we do have evidence (direct or background), and then we are not ignorant (even if we might be wrong, we must work with the information we have). I give examples of this for the criterion of embarrassment, and discuss what is necessary to make such an argument work, throughout pp. 158-69. Otherwise, our assumptions just fail to be generalizable, e.g. the usual intuitions you hear from Jesus scholars would entail the castration of Attis should have been too embarrassing for his followers to invent, yet they obviously invented it anyway. Thus, evidently our intuitions on this point just suck. We therefore cannot rely on them.

This does not mean no argument can be made. I detail just how to make one work. But that it can be done in principle is not the same thing as it having actually been done. I await a truly sound argument from embarrassment to the historicity of Jesus. Once a scholar knows how to do that non-fallaciously, if there is still something left over that still yet points toward a historical Jesus, that would be progress in my view. Hence I welcome it. Proving History lays out how that can be done. If it can. And that depends on the actual evidence we have. So we’ll see.

McGrath also misses the whole point of my argument on pp. 162-68, where I mathematically demonstrate that apparently embarrassing stories in the Gospels have a low prior probability of being true (exactly contrary to our intuition). He reacts to this by saying:

Carrier claims that anything included in an early Christian work must have been worth including and therefore could not have been embarrassing. But by this token, any detail in any text seemed worth including to its author, and could therefore be deemed suspect.

That’s not my argument. I carefully explain that my argument applies to (1) friendly (2) propagandistic texts (3) that lack internal indications of embarrassment–that’s three criteria a text has to meet in order to fall to the analysis I provide (see pp. 162-63; note also my preliminary demarcation between sober history and propaganda on pp. 160-61; and my discussion of actual examples of demonstrated embarrassment in the Gospels on pp. 131-34).

Hence McGrath falsely generalizes a finding I reach for that subset of texts, to all texts whatever. That’s incorrect reasoning. Moreover, he fails to interact with my mathematical demonstration of the point: the only way he can conclude I am wrong, is to find where I go wrong in that math. But the math is pretty solid. So the conclusion is well established: the Gospels would not likely include any embarrassing material unless it served a purpose that would just as easily warrant its fabrication in the first place (a general point I had already discussed on pp. 134-37).

By contrast, McGrath refers to my remark elsewhere that “the absence of any likely or discernible reason for the story as we have it to have been made up (by the historian or his source),” which is one of several criteria (note: one of several; it’s not always going to be sufficient on its own) that we can apply to warrant a priori trust in a report (p. 253). Yet note that my section about the Gospels explains why there are several reasons for stories in them to be invented. Thus, we are not in a condition of “the absence of any likely or discernible reason for the story as we have it to have been made up (by the historian or his source),” so McGrath is misapplying the latter rule. In fact I show that we have a general reason to expect all the stories in the Gospels had such a reason for their composition (or that most did: since my argument is probabilistic), even when we do not know what it is specifically.

A mundane example (not connected to embarrassment) is the number of fish counted in the miraculous catch in John 21:11 (the number is 153). Only a rank fundamentalist would believe that this actually happened, and Peter actually counted out 153 fish, and that this meaningless detail was transmitted over half a century of oral storytelling for some indiscernible reason. No, there was some reason for this number (and indeed the whole story) to be fabricated. That is obvious even without knowing what that reason specifically was (I know what some of those proposed reasons are; my point is that knowing any of them isn’t even necessary to reach this conclusion). And as in this case, so in all cases of alleged embarrassment–as I argue and demonstrate at length.

McGrath simply doesn’t interact with my argument in this case. At all.

Dying Messiahs

McGrath has been burned on this before (see recap), so he clearly struggles to parse his words this time, trying to thread the byzantine needle of dogma he wants to maintain. I’ve already discussed the evidence extensively in The Dying Messiah Redux (fully revised and updated) so I won’t reiterate the evidence and argument laid out there. McGrath says this time:

[Carrier] also continues to discuss whether “messiahs” (i.e. anointed figures like kings and high priests) could die – something that no one to my knowledge has ever disputed – rather than focusing on the smaller set (again, as his Bayesian approach requires) of the specific type of anointed one that the earliest Christians claimed, namely a Davidic anointed one, the figure expected to restore and rule the kingdom of his forefather David. There is no text from this period which suggests that the individual of Davidic descent who was expected to restore the dynasty of David to the throne was also expected to fail before achieving that by getting executed by foreign rulers.

Notice how ultra-specific he has to make his definition of “messiah” to create any kind of objection to what I actually argue. He claims this is what a Bayesian approach requires, but that’s exactly backwards. Creating hyper-specific definitions in order to avoid the consequences of generalizations you don’t like is not sound reasoning. In fact McGrath makes no effort to construct an actual Bayesian argument for his conclusion contrary to mine. And that’s the poster child for abusing Bayesian reasoning: claim your argument is Bayesian, and then do nothing whatever to show how or why it’s Bayesian. Don’t do that.

McGrath is also confusing what I argue in the book (that theories like this have to be properly examined and ruled out before being dismissed) with what I have argued elsewhere (that this theory is probably true). He apparently has no real argument against what the book says, and instead insists the problem has been sorted, when in fact it has not. We have several texts showing that the Jews did indeed imagine dying messiahs presaging the end times. That’s all the Christians needed. Because all one has to do is combine that, with the idea of restoring a new world order (as they believed Jesus would do in the future), to get Christianity. And as I’ve explained before, we simply cannot rule out this possibility. Not on present evidence, which is far too scarce (as I and other scholars have pointed out: again, see my remarks above).

In Bayesian terms, as I’ve explained before, the probability that someone would invent the kind of messiah McGrath is talking about is zero (because everyone would notice the total lack of military triumph over the Romans, therefore such a thing could not be invented), which entails that if Christians invented their messiah, the probability that he would be a messiah whose victory is invisible, like the messiah who dies in the timetable of Daniel 9:24-27 (which “predicts” the last messiah’s death before an imminent end of the world) in order to perform a celestial temple-cleansing (as in Hebrews 9), is virtually 100%. Indeed, an imaginary dying-and-rising messiah is precisely the kind of messiah Jews were likely then to invent, if they were to invent any, given the growing multicultural fashion for saviors of just such a kind.

McGrath seems to want to make an argument from prior probability, such as that Jews tended not to do things like that, but that is where the problem of ignorance kills his argument: we have no business claiming to know what Jews did or did not tend to do, given that there were dozens of sects at the time, and we know barely anything about even a handful of them, much less all of them. There is simply no data for McGrath to build a reference class that gives him the kind of “low prior” he seems to want.

This would be the wrong way to go about it anyway, since (a) we have to start with a prior probability based on the best data-set we have for building a reference class (Proving History, pp. 229-53, esp. 233), and (b) the evidence establishes the Jews of this period were actually very innovative, and minor sects very iconoclastic (as in, ready to abandon, reinterpret, or turn upside down views pressed by the elite orthodoxy), so the prior probability of an innovation of this kind isn’t going to be low. We have to look elsewhere to argue against it (if we are bent on doing so).

Thus, McGrath misses the point when he concludes:

The only way to argue that this was more likely invented is to say that anything in a text could be invented – which is true, but it is not a valid piece of Bayesian reasoning. This is true of all texts, in theory, and an “explanation” that can fit any evidence has little or no explanatory value in and of itself.

This is all wrong. This is in no sense “the only way” to argue the gospel was more likely invented. And I certainly never endorse the argument “could be, therefore was.” In fact I explicitly denounce that reasoning (Axiom 5, pp. 26-29). To the contrary, I explain what “the only way to argue” for ahistoricity is on pp. 117-19 and 204-205, and McGrath does not mention what I say there at all.

McGrath instead goes on to say:

The question is whether it is more likely that a group who followed a messianic claimant of the sort we know appeared in this period in history made sense of his failure by giving his execution of positive interpretation, or whether it is more likely that a group invented a purely fictional failed Davidic anointed one and set about trying to persuade their contemporaries to believe in him. To every scholar with a substantial background in early Christianity or ancient Judaism, the choice seems a no-brainer.

This is precisely the problem: scholars refuse to properly examine the alternatives with a proper method because of their fallacious, methodologically-unsound, dogma-prone assumptions. It’s “a no-brainer.” Therefore we don’t even have to make any valid argument against it. We just, uh, “know it in our bones” or something. That’s the exact opposite of Bayesian reasoning.

The question indeed is precisely what McGrath describes: what best explains the evidence (all the evidence) we have, that an actually executed man inspired it all (as the canonical Gospels claim), or revelations of a self-sacrificing archangel inspired it all (as Hebrews 9 and the earliest credible redaction of the Ascension of Isaiah claim)? That cannot be answered from the armchair, much less with dogmatic assumptions about the ideological bullheadedness of Jews, who (I guess we’re supposed to believe) could never innovate their way out of a paper bag, much less a real socio-theological crisis like the Roman occupation.

McGrath shows his enslavement to dogmatism most explicitly when he says:

If Carrier’s method can take such relatively straightforward mundane statements [that Jesus was born of a woman, under the law, and of the seed of David], and claim that they more likely refer to things that transpired in a celestial realm, then Carrier will have showed that his method does nothing to add rigor to historical study.

Here McGrath asserts dogmatically that such a conclusion can never be demonstrated. Before he has seen any argument regarding it. This is the opposite of Bayesianism. If it is a priori impossible for McGrath to be wrong about this, then he is cutting himself off from ever discovering his own incorrect conclusions. No method could ever persuade him, because, well, he can’t possibly ever be wrong. That’s dogmatism, not scholarship.

The first rule of being a Bayesian is: you can always be wrong. McGrath has failed to learn so basic a lesson as that. Bayesianism tells us that all arguments can be reduced to a dispute over just three numbers. Until he is willing to actually engage such a dispute, his assertions of certainty are unfounded, and exemplify all that is wrong with Jesus studies today.

Nazareth vs. Scholarship

McGrath makes the following bad arguments regarding the problem of the origin of Jesus being called a Nazarene (besides not engaging with any of the actual arguments and scholarship I discuss on the point, pp. 142-45, which is already an alarming failure to properly engage with my work, and another example of his dogmatism), which I have made easier to reference by numbering them:

On the one hand, [Carrier's] use of Rene Salm’s self-published armchair opinions (p.142) is at variance with [1] his emphasis on both the need for relevant expertise (Salm has no qualifications or experience relevant to either the archaeological or the linguistic matters on which he comments, and regularly gets things wrong), and [2] the appropriateness of ignoring fringe claims with little probability of being correct when doing Bayesian calculations. [3] Carrier’s own linguistic deficiencies become apparent when he treats Irenaeus’ account of the symbolic meaning given by Gnostics to words as indicative of the actual meaning of those words (p.142). While there is a legitimate line of investigation about the relationship between the various forms of Nazareth and terms allegedly associated with it (in particular Nazorean), [4] without the relevant background in Semitic linguistics, the matter is not going to be given a plausible explanation, and because of his lack of background and expertise in this particular area, Carrier seems unable to discern when Salm is offering him bunk packaged to look to the non-expert eye like scholarship.

Let’s take these in order:

[1] First, McGrath ignores my explanation in Axiom 12 (p. 36) that we can cite non-scholars when they make arguments we (as experts ourselves) verify are worth examining. That Salm gets some things wrong is not a valid argument to dismiss everything he has said on this point, not least because his argument has appeared in a peer reviewed field-relevant academic publication (Bulletin of the Anglo-Israel Archaeological Society 26 [2008], with rebuttals by his peers), which McGrath just got done insisting mythicists should do. So here, Salm does what McGrath wants mythicists to do, but then that’s apparently not good enough, and so even his properly submitted peer reviewed work is to be dismissed without even examining it. McGrath is the one not living by his own principles here. My use of Salm is entirely consistent with mine.

Second, McGrath strangely fails to mention that I back Salm’s work up with that of other peer reviewed articles and bona fide experts, including Eric Laupot, J.S. Kennard, and Robert Price, as well as actual ancient evidence (none of which McGrath mentions or addresses). Moreover, McGrath fails to mention that I explicitly state that “I do not agree with all the theories of either Salm, Kennard, or Laupot” (p. 142). In particular, I believe, and have said this repeatedly in public, that Salm is wrong to conclude there was likely no Nazareth in the time of Jesus, and I mention no such argument in my discussion in Proving History. So if McGrath is trying to impute that to me, that’s dirty pool, and a plain violation of Axiom 12 (pp. 34-37), deploying the very “baggage fallacy” I explicitly warned readers against. McGrath should be a better student than that.

[2] McGrath says that some unstated theory (note that he does not say what) is a “fringe claim” that has “little probability of being correct when doing Bayesian calculations,” but then does no Bayesian calculations to show this. Once again he is abusing Bayes’ Theorem by claiming it gives us a conclusion, without showing how, or even giving any indication that he knows how. He just dogmatically asserts that the conclusion must surely go his way, even though he makes no attempt to find out. Indeed, he doesn’t even state what the claim is that he can somehow show by some undescribed Bayesian analysis has “little probability.” That is not scholarship. It’s argument by dogmatic assertion.

[3] McGrath betrays his failure to read endnotes when he says “[Carrier] treats Irenaeus’ account of the symbolic meaning given by Gnostics to words as indicative of the actual meaning of those words.” I wrote (on p. 142) that Ireanaeus “believed” Nazaria meant Truth in Semitic, and in the associated endnote I state (n. 49, p. 315): “We do not know of any such word; more likely the actual derivation was from something else, like natsar, as perhaps “keeper of secrets” (i.e., the mysteries; by derivation from, e.g., Isaiah 48:6 and 42:6), which Christians proclaimed (and thus equated with) ‘the truth’.” Thus I very explicitly did not treat Irenaeus’ observation as “indicative of the actual meaning of those words.”

[4] But I did cite the Gospel of Phillip as confirming what Irenaeus thought, a fact McGrath also fails to mention, despite the fact that this is the only claim I cited Salm for, and it is unmistakably true. So McGrath’s red herring fallacy, claiming Salm gets facts wrong, therefore he got this fact wrong, looks borderline dishonest to me. There is not a single thing I cite Salm in defense of that isn’t demonstrably correct. Evidently that ruins McGrath’s storyline, so he won’t think to tell you that. Instead, McGrath says Salm offered me “bunk.” Well, no. What I cited him for is fact, not bunk. And I got the linguistic details right, despite McGrath claiming I didn’t.

By contrast, McGrath commits an obvious fallacy when he argues from “the ‘prophecy’ Matthew appeals to here [predicting Jesus would be a Nazarene] is not found in any known Scripture” to the conclusion that Matthew invented that prophecy. That’s a non sequitur. Matthew would sooner invent a prophecy naming a town, not an epithet that has no evident connection to a town, and then try to pass that off as predicting a town (and Matthew, a Torah-observant Jew making arguments directed at fellow Jews, would not be so stupid as to try to pass off an invented scripture, much less expect such a thing to be a convincing argument to them). We know for a fact the Christians used scriptures we no longer have, and scriptures we do have but with variant readings and verses we don’t have (the epistle of 1 Clement is full of examples of scripture citations we can’t identify, for example; and many more examples can be found throughout the second century church fathers). Thus, McGrath cannot argue from “he cited a scripture we don’t have” to “no such scripture existed.”

It’s ironic that he follows this ignorant fallacy with the conclusion that I don’t know what I’m talking about, when obviously he’s the one who is not up on basic field-relevant facts like this.

Jesus as a Judeo-Pagan “God”

McGrath mentions having other criticisms, but doesn’t give any specifics, so there is nothing more to respond to, as regards the merits of Proving History.

But some of his half-formed criticisms seem to be allusions to things not in Proving History. At one point, for example, he writes about my theories regarding the reference to James “the brother of the Lord” in Galatians, even though I don’t discuss that anywhere in Proving History. And though McGrath says of this issue that “Carrier falls back on arguments that do not reflect the rigorous Bayesian logic he calls for historians to use,” he does not demonstrate this, or even explain what he means. In fact I have toyed with Bayesian models for answering this question. So what am I failing to do, by his estimation? It’s not like he couldn’t build his own actual Bayesian argument for whatever conclusion he wants to maintain here. That’s the only way to make progress. Whereas making vague, unsupported claims of methodological errors that are never identified is of no use to anyone.

Similarly, at another point, he remarks that “[Carrier] even continues to make reference to the long-discredited idea that Jesus was thought of as ‘God’ or ‘a god’ by his earliest followers,” which I can only assume is a parroting of that claim in Ehrman’s latest book, which ignores entirely what I actually say about this in the work in question (which is not Proving History, but Not the Impossible Faith, chapter 9, pp. 247-57), where I explicitly articulate the view that the first Christians did not equate Jesus to God, but as an adopted son and agent of God, one who represents God, as all kings, high priests, and prophets of God did. That Ehrman didn’t pay attention to what I actually argue in the book, and McGrath just bought Ehrman’s mischaracterization of it, demonstrates why we can’t rely on Ehrman’s treatment of mythicist authors in general (and that’s not the only thing wrong with Ehrman’s book on the subject).

And yet McGrath overlooks the fact that Jesus was still more than that. He is a pre-existent celestial being with the assigned powers of God in our earliest texts: e.g. Philippians 2, 1 Corinthians 8:6 and 15:24-28. Which means he would have been in pagan parlance a god–what Jews typically called an archangel, a type of being pagans only understood as a deity. The notion of an “archangel” was a peculiarly Jewish way to have gods without calling them gods; the closest equivalent in pagan parlance was Lord, kyrios, the exact same thing Christians called Jesus, a word that was for pagans simply a synonym of “god” when referring to celestial powers, as Christians understood Jesus to be in our earliest recorded texts.

Thus, there were two systems of vocabulary in antiquity, and when translating from Jewish to pagan thought-concepts, Jesus would have been understood as a god from the beginning–just not the God, a hugely important distinction, even for pagans. Christians would not consider Jesus to be the God until well into the second century (at the earliest); but they already considered him a god from its earliest recorded time, if we use pagan but not Jewish vernacular.

For example, Paul slips into pagan vernacular when he calls Satan a god (2 Corinthians 4:4); obviously if Satan could be called a god, so could Jesus, who was his celestial superior. It just depended on whose vocabulary Paul chose to employ. For example, in contrast to the pagan, Jewish vernacular made a distinction between “deities” and “gods” (1 Corinthians 10:20: “the things which the Gentiles sacrifice, they sacrifice to demons [daimonia, "deities"], and not to God”), which made no sense in pagan vernacular, where these were synonyms. More exactly, the words Christians and Jews used for “demon” were two in number, daimôn and daimonion, the former meant “deity” and was applied to gods of all rank by pagans (it’s simply a synonym of theos), while the diminutive daimonion more often meant deities of lower rank (i.e. subordinate gods). Other than the fact that occasionally daimôn could be used in a related sense, distinguishing demigods from full gods (but both still gods in modern parlance), making this distinction between theos and daimôn is a Jewish invention, a way to continue having many gods while still appearing to be monotheistic. “Good” gods were angels; “bad” gods were demons. But they are all still “gods” by any pagan definition of the time (and to be honest, by our definition today, when speaking of gods generally instead of God specifically).

About one thing McGrath is right: understanding this context is crucial to understanding the origins of Christianity.


  1. bobwahler says

    Particularly as there really is plenty of crazy coming from mainstream scholars even in mainstream venues (I’ve mentioned my bafflement at Robert Eisenman’s bizarre theories about the origins of Christianity before, for example, and I needn’t mention that pretty much no one in the field buys them, either), so it’s not like mythicism would really be so out of place there (it’s just dogmatically opposed with more fury; theories like Eisenman’s apparently get a pass because at least they still have a historical Jesus in them).”

    Bafflement, Richard? Perhaps I can help. I’m still waiting for anyone to show just where Eisenman is wrong. I know Eisenman personally, and he was an inspiration for my own work. Let’s start with GEZA VERMES. When comparing translations, hands down, Eisenman wins. He has the correct, “They afflicted him with the Judgements upon Evil and inflicted upon him the outrages of Evil pollutions in taking Vengeance upon the FLESH OF HIS CORPSE” at 1QpHab IX:1-2, the Habakkuk Pesher. “Its interpretation concerns the Wicked Priest, whom as a consequence of the Evil he did to the Righteous Teacher.” -IX:9. Vermes has the redundant “body of his flesh”, showing his misreading of the atrocities inflicted on ANANUS for what he did to James. It is this sort of internal indicator, AND NOT THE CARBON DATING, which is inexact, which puts the Pesherim in the First Century CE, not BCE, like Vermes, et al, want it to be for the Maccabean era. “They come one after another” refers to the Kittim leaders of the Imperial Roman period, not Vermes’ Republican Triumverant period. The “violence done to the land, the township and ALL ITS INHABITANTS” (IX:8), “destroying many by the Sword” (VI:10), and “sacrificing to their standards” (VI:4) is Titus, not Pompey, first century CE again, not BCE. Pompey was notoriously gently compared to what happened under Titus and Vespasian. You need to understand what the author of the Pesherim was doing when he said things like “Woe unto him who builds a CITY ON BLOOD and establishes a township on Unrighteousness”, referring to the “Spouter of Lying” who is “leading many astray” by “removing the Boundary Markers” of the Law. He shows every which way but Sunday how this is PAUL, and no other!

    He says, regarding reference to a contemporary of Alexander Jannaeus, Demetrius, being Greek, not Roman in the Nahum Pesher as the consensus attempts to push back the dating 100 to 150 years, that this is retrospective: “However, a careful literary/historical examination of this text will demonstrate it to be retrospective and historiographical in nature and support the opposite conclusion.” page 132, “The Dead Sea Scrolls and the First Christians”.

    I could go on, but why? He wrote 3,000 pages to hit doubters over the head with copious proofs. It isn’t his fault if you can’t follow it. I did.

  2. stoferb says

    About argument from embarressment. If Jesus was a historical person shouldn’t we expect to find only a few ‘embarressments’ no matter how many more details didn’t fit? Afterall the early christians would only be interested in mentioning things that could be easily reconsiled.

  3. keithwerner says

    Considering that they had Bart Ehrman on recently being (among other things) casually dismissive of both you and Robert Price, I wonder if the folks over at the “Unbelievable?” podcast would welcome having you on their show to discuss “Proving History”?

  4. Paul Doland says


    Have you addressed “A Mathematical Review of Proving History”? Seems to be by somebody named Ian, but, the article has no byline.

  5. kyoungers says

    Dr. Carrier – You called out this passage in McGrath’s review:

    “Carrier claims that anything included in an early Christian work must have been worth including and therefore could not have been embarrassing. But by this token, any detail in any text seemed worth including to its author, and could therefore be deemed suspect.”

    I read the review and this part made me double-take. He seems to be saying that your argument is “Not proven to be embarrassing ==> untrue,” whereas I thought your argument was more like “Not proven to be embarrassing ==> not proven to be true by way of the criterion of embarrassment,” which obviously is not the same thing. Is he really actually that wrong, or am I misinterpreting?

    I’m a new commenter (still slogging through Proving History … about 1/3 through chapter 6 as of now), so if I am off base, be gentle. :) Often it’s hard for me to read a negative review of something that I’m inclined to agree with, because I don’t trust myself to be perfectly objective in analyzing it.

    • says

      No, I don’t think that’s what McGrath meant to say. I assume he means just “not true by way of the criterion.” But certainly, if he means to say that I argue “there is always a reason to invent a detail, therefore every detail is invented,” then that’s double wrong, for the very reason you note.

      I only argue that there being a reason to invent a detail constitutes a valid alternative hypothesis that must be ruled out, and Bayes’ Theorem is the only way to go about doing that, if it can be done; the mere criterion of embarrassment is completely impotent to deal with situations of multiple competing hypotheses with differing likelihoods. Thus the method of criterion itself is not logically sound.

      I also argue, in the matter he is referring to (where I detail various conditions and exceptions, so he is fatally oversimplifying), that the prior probability that seemingly embarrassing material in the Gospels is true is low (this does not hold for all kinds of documents, however), even when we don’t know why it’s in there (i.e. even when we don’t know what the best alternative hypotheses specifically are). However, that’s just the prior. As you’ll know from my explanation of Bayes’ Theorem, a good enough balance of consequent probabilities can overwhelm a low prior, so a story’s truth having a low prior probability is not equal to it being false.

      That is, however, a common mistake people make who are new to Bayesian reasoning, so it’s possible, I suppose, that McGrath made that mistake. I don’t know.

  6. blotonthelandscape says

    Not finished reading, quick typo:

    (by the historian or his source,”

    under “Embarrassment Criterion” should be inverted commas, not parenthesis at the beginning.

    • says

      I’m not seeing what you mean. “by the historian or his source” is and should be enclosed in parentheses; the quote, on the other hand, ends at the end of that but begins several words before that parenthesis begins.

  7. Roo Bookaroo says

    Excellent article, as usual. Superb control of argumentation logic.

    However, you seem to rely too much on the concept of “pagan”, which is a Christian view of culture, defining an abstract world that lived “on the outside”, but in fact never existed except in a Christian imagination.

    Whereas your real analysis as a historian, in this very article, focuses on the “Greek” mind, “Greek” parlance, the “Greek” vocabulary, the “Greek” thought-concept, Paul slipping into “Greek” vernacular, etc…All the words you use as examples are “Greek” words, not pagan words. There was no pagan language, only in Christian abstract imagination.

    Every time you mention “pagan”, an abstract word referring to no specific reality, we must substitute “Greek” to make your text concrete and historical.

    One major problem with historical criticism of the origins of Christianity is that most scholars attracted to this field come from a Christian background, or a Christian impregnated culture, and are often unable to free themselves from the baggage of Christian concepts and Christian imagination they bring along from their Christian past. R. Joseph Hoffmann is a typical case.

    The concept of “Pagan” definitely belongs to that baggage, and it only obscures the real description of facts and events.

    It is also the case of most non-professional blogs dealing with the question of Christian origins, mostly from amateurs who use their blogs to come to terms with their own past indoctrination in Christian ideology. They like to speak of “our” Mark, “our” Luke, as a given. Why not “our” Homer, “our” Virgil, “our” Lucretius, “our” Shxpr?

    And it is not acceptable to shrug this source of confusion off, as some of those amateur bloggers do, untrained in linguistics and the hard analysis of philosophy, by claiming that language is “fluid”, that concepts remain “blurry” at the edges, and that it does not matter, “as long as we understand each other”.

    • says

      That’s true, “pagan” is just a modern concept that we use to conveniently demarcate different worldviews in antiquity. In the field of ancient religious studies it simply means “standard polytheists” which means, in effect, “neither Jewish nor Christian.”

      Thus, when I speak of “pagan” vernacular I am not talking about “Greek” vernacular–because many monotheistic Jews spoke and wrote Greek, whereas many “pagans” spoke and wrote, for example, Latin, or any of several other languages. I am talking about the vernacular common to typical polytheists within the Roman Empire at the time. “Greek” as a term is therefore wholly incorrect for this purpose and thus is not representative of what I am talking about, any more than “Latin” or “Celtic” or “Persian” would be. “Pagan” is the term used in this field. That it originates within a Christian culture is no more significant than the fact that it originates in the English language, which also did not exist two thousand years ago.

      The relevant matter here is that yes, polytheists had a distinct vernacular; so did Jews; and so did Christians, by the second century. I gave an example in this article, which is a genuine example of differences between those vernaculars. The use of the modern field-idiomatic term “pagan” makes no difference to that point.

  8. victortanner says

    There’s a typo in the paragraph about the miraculous catch of fish in John 21. Both 153 and 253 are cited as the number of fish caught.

    • says

      In what manuscript does 253 appear? The standard Aland critical apparatus shows no variants for that passage (Jn. 21:11). I know there are variants in manuscripts they fail to include, so I wouldn’t be surprised if they forgot this one, but I also checked the Swanson concordance (which often includes variants that the Aland text omits) and it doesn’t note any such variant either. So I am curious to know where such a variant is.

    • jimroberts says

      You are the author of the variant: “number of fish counted in the miraculous catch in John 21:11 (the number is 253).”

    • Jesse M. says


      You have misread Tanner. He said that, when you discussed the number of fish, you made a typo because you cited two different numbers when only one number could be correct. However, Tanner misread your paragraph because you said that “the number was 253″ but then say (as a matter of correction) that “Peter actually counted out 153″. Hence, you did not make a typo.

      In your blog entry, you did not give a reason or citation for the number 253. The first time I read the paragraph, it seemed that you were citing John 21:11, which would be wrong, but it became clear on the second time I read the paragraph that you did no such thing, at which point I seen there was no citation, at which point I suspect that John 21:11 was supposed to be a citation, at which point I suspected a typo (i.e., that you meant to write 153), at which point I read the paragraph a third time and seen that there was no typo, which means there is no typo and no citation. I checked the comments to see if you said anything about the number and found your reply here in which you express that you have no knowledge of 253 ever appearing in a manuscript, which makes the matter more puzzling — where did that number come from and why did you mention it?

      (Given what Tanner and I have said, I think you might want to revise that paragraph to make the text easier to read and the reasoning easier to follow.)

    • Drew says

      Richard, I think victor meant that you had made a typo in the paragraph above referencing the fishes. You first write the number is 253, and then you later write the number is 153.

      Emphasis added

      A mundane example (not connected to embarrassment) is the number of fish counted in the miraculous catch in John 21:11 (the number is 253). Only a rank fundamentalist would believe that this actually happened, and Peter actually counted out 153 fish, and that this meaningless detail was transmitted over half a century of oral storytelling for some indiscernible reason.

    • says

      Unfortunately I rarely have time to participate in comment threads on other blogs, but he is welcome to voice his criticisms here if he deems them important. Or you can quote or point me to specific ones here and ask about them.

    • noen says

      Basically he says that you don’t know what you’re talking about. You don’t understand Baysian reasoning and even if you did it doesn’t apply to history. Seems like par for the course if you ask me.

      I have never in my life met a group of people so arrogant and insular as the so-called online atheist community. Your own past behavior on this blog where you attempted to defended insults and slurs and where you have made grossly intemperate remarks worthy of the worst authoritarians in history has done little to improve your standing in my estimation.

      On the historicity of Jesus your position amounts to little more than a conspiracy theory. Indeed, that is the typical atheist account of religion from what I can tell. It’s all some vast conspiracy by priests to enslave the minds of their followers.

      We have historical accounts of a person called Jesus who some Jews of the day considered to be their messiah. There is good reason to reject their latter claim but little to reject the former. Why should we believe that a Roman historian falsified history? What motive would he have for doing so? If a local historian, in my case that would be Hy Berman of the U of M, talks about someone in Minn. history I have no good reason to doubt that person existed. I might doubt extraordinary claims made about that historical figure but the testimony of a historian seems to me to confer the benefit of the doubt to that person’s historicity.

      The educated classes of the Roman Empire were little different than we are today. They knew the world to be round even though they had a bad theory for the solar system. The practice of historians then as now is little different. They were intelligent, conscientious professionals who took great pride in their craft.

      I have no more reason to doubt the historicity of Jesus than that of Alexander the Great and every reason to doubt the legendary tales of both. This is a perfectly reasonable conclusion to reach and you have done nothing to convince me otherwise. Indeed, your intemperate behavior in the past causes me to doubt your ability to think clearly in other matters. If you cannot handle criticism and believe that there is a conspiracy to marginalize you among professionals…. well, it gives one pause.

      From Irreducible Complexity regarding prior background knowledge:

      “In this Carrier allows himself to sidestep the question whether these necessarily true conclusions are meaningful in a particular domain. A discussion both awkward for his approach, and one surely that would have been more conspicuously missing if he’d have described why BT is the way it is.”


      “This is not wrong, per se, but highly bizarre. One can certainly bundle the claim and the event like that, but if you do so Bayes’s Theorem cannot be used to calculate the probability that the claim is true based on that evidence. The quote is valid, but highly misleading in a book which is seeking to examine the historicity of documentary claims.”


      “Carrier joins that latter debate too, in what he describes as a “cheeky” unification of Bayesian and Frequentist interpretations, but what reads as a possibly independently conceived (certainly uncited and unnuanced) statement of a multiple-words interpretation of Bayesian probability. Describing what this means is beyond my scope here, but I raise it because it is illustrative of a tone of arrogance and condescension that I consistently perceived throughout the book. To use the word “cheeky” to describe his “solution” of this important problem in mathematical philosophy, suggests he is aware of his hubris. Perhaps cheeky indicates that his preposterous claim was made in jest. But given the lack of mathematical care demonstrated in the rest of the book, to me it came off as indicative of a Dunning-Kruger effect around mathematics.”

      I think that the hysteria and arrogance of the online atheist community has impacted your reasoning. I think that is true of a great many of today’s atheists. You begin from a place of high emotions in reaction *against* religion and then engage in motivated reasoning to justify your prejudice and bigotry.

      If what I say is true then all you will succeed in doing is to destroy the very thing you claim to hold in high regard.

      And it can’t come soon enough as far as I’m concerned.

    • says

      Your own past behavior on this blog where you attempted to defended insults and slurs and where you have made grossly intemperate remarks worthy of the worst authoritarians in history has done little to improve your standing in my estimation.

      Ah, hyperbole. My favorite fallacy.

      Oh, and it’s a twofor, too! Not only the fallacy of hyperbole, but of ad hominem (“Carrier is a dick, therefore he is not a competent scholar and his ideas are wrong”).


      On the historicity of Jesus your position amounts to little more than a conspiracy theory.

      Actually, my theory involves no conspiracy theories. But then, maybe you don’t know what a conspiracy is. If you are confusing (A) “people doctored evidence” with (B) “the papacy (?) conspired to doctor evidence,” then you have committed a fallacy of equivocation with the use of the word “conspiracy.”

      Because (A) is a documented fact. There are over 40 known Gospels, almost all of which are unanimously agreed to be forgeries; likewise almost all the Acts written, of which there are some half dozen; even roughly half the epistles in the NT are universally agreed by experts to be forgeries. The number of established (as in, confirmed) interpolations discovered in biblical manuscripts (counting those that aren’t included in any published translation and aren’t even mentioned anymore in standard apparatuses) is in the hundreds.

      So if all you are talking about is that mythicism requires assuming some Christians lied, a lot, then we have all the evidence on our side. Even Bart Ehrman himself agrees with that premise, and is one of its most avid defenders (see Forged). But if you are talking about some weird conspiracy theory beyond that, then I don’t know what you are talking about with respect to me. I’ve never advanced such a theory.

      Why should we believe that a Roman historian falsified history?

      Which historian are you talking about? We have no Roman historian reporting anything but what Gospel-reading Christians told them. As far as they assumed, they were reporting the facts. They had no practical way of checking to discover the Gospels were fabricated, any more than they could do the same with the myths of Romulus–yet Plutarch “records” the life of Romulus as a historical fact, even though no such person ever existed. Plutarch just didn’t know any better. He had little ability to distinguish myths from histories, and no access to the data he’d need to tease them out. We now do (e.g. we can now see that the Romulus myth is based on an earlier Greek myth, and originated centuries after Romulus is supposed to have lived; likewise, Romulus is an obvious mythical name, and his role in originating Rome contains numerous hallmarks of mythic invention, etc.).

      The practice of historians then as now is little different.

      False. Catch up on the real expert facts in this matter, e.g. Greek and Roman Historians: Information and Misinformation, just for starters.

      They were intelligent, conscientious professionals who took great pride in their craft.

      Yet lacked anything like the standards, methods, resources, or background knowledge that we do. They were, by modern standards, sloppy and careless and prone to believing any story they liked and typically too lazy to do very much of what we call “fact-checking.” They were also routinely prone to making facts and stories up, because they were “sure” they were true or because they made a good story or communicated some moral or political fact they wanted to illustrate. This is well understood across the board for all ancient historians, even the supposed gold standard among them, Thucydides (who even confesses to mostly fabricating the speeches he includes in his history). And was understood even by themselves, as illustrated by Lucian’s On How to Write History, which not only reveals how commonly historians were failing even at his standards, but also how low his own standards were compared to ours now.

      Not that any of this matters to the historicity of Jesus, as no ancient historians record any facts pertaining to the existence of Jesus, other than that there were second century Christians who believed it. Which is not useful to us. There were second century pagans who believed in the historicity of Hercules and Romulus, too.

      I have no more reason to doubt the historicity of Jesus than that of Alexander the Great and every reason to doubt the legendary tales of both.

      Bad analogy. The evidence for A the G is vast and superb, including abundant contemporary attestation in historians and speeches and other documents and writings, in inscriptions, coins, archaeological finds, and a surviving summary of three eyewitness accounts. If we had that for Jesus, I quite agree, his historicity would be decisively established.

      This is a perfectly reasonable conclusion to reach and you have done nothing to convince me otherwise.

      I never claimed I did. My book on this hasn’t been published yet. Indeed, I have repeatedly said, in public, in many venues, that this is only a hypothesis worth considering and that people like you should assume historicity until a larger number of experts in the field begin to concede it’s uncertain. That actually is starting to happen. But my book next year will be the first best attempt to make clear why it should, in terms experts in the field will respect and understand.

      So you must be confusing me with other mythicists. I have always said that I am against the notion that we should insist Jesus didn’t exist and claim that belief otherwise is always automatically unreasonable. Rather, we should maintain that it’s debatable, and worth having a serious and informed debate over it. That’s not the same thing. And bad arguments for his existence are unreasonable. But there is a difference between saying that, and saying belief in historicity as a whole is unreasonable. It may be. But that has yet to be properly determined by a reasonable and informed debate.

      Saying we shouldn’t even have that debate is what is unreasonable.

      If you cannot handle criticism and believe that there is a conspiracy to marginalize you among professionals…. well, it gives one pause.

      Actually, I have repeatedly demonstrated my ability to handle criticism and revise my positions in response to it. Not only in general, but in this specific subject.

      As to the rest, I don’t believe there is an organized conspiracy to marginalize us, but there are documented attempts to do so by individual actors.

      From Irreducible Complexity regarding prior background knowledge…

      None of your quotes included any context as to what claims of mine were even being discussed. There is therefore nothing in your quotations for me to respond to.

      Nor did they even seem to contain any actual arguments against what I say, just irrelevant declarations of the supposed arrogance of my arguments (which has nothing to do with whether they are actually correct).

    • Waffler, of the Waffler Institute says

      I found the “Mathematical Review” to be anything but illuminating. The chief (mathematical?) problems he found seemed to be 1) that Proving History had an idiosyncratic (but not wrong) formulation of Bayes Theorem in it, and 2) that it was possibly being condescending in said formulation.

      He also claims, without any real explanation, that certain claims in the book are ‘laughable’, and that Bayes Theorem just can’t be used to answer certain questions.

      But he doesn’t really engage the mathematics at all.

  9. sawells says

    I guess McGrath’s review does show some understanding of Bayesian thinking: the constant hints — that of course a fictional Jesus is a silly idea and of course there was a historical Jesus, yes Virginia — are supposed to ensure that his audience place a low prior probability on mythicism. Thus he will save some of his flock from placing a high posterior probability on mythicism when they are exposed to the wiles of the tempter, viz. you :)

  10. stuart says

    I think a historical Jesus is the best explanation of the facts, in particular, the fact that people apparently ‘saw’ Jesus after his death. We know that bereavement can cause hallucinations. We also know that physical strain can cause hallucinations, for example, it’s common for mountaineers and arctic explorers to hallucinate. The disciples first suffered a bereavement then had to make an arduous journey from Jerusalem back to Galilee. These are ideal conditions for inducing hallucinations. It’s interesting that Paul also supposedly ‘saw’ Jesus while travelling a long distance, which in those days was no trivial business.

    On the other hand, we have no knowledge about any conditions that might have caused people to see a purely imaginary being.

    • says

      Unfortunately, your hypothesis fails to explain the very example you use: Paul. That cannot have been a bereavement hallucination. If Paul could hallucinate a Jesus he never personally met, so could Peter or anyone else.

      You are right that fatigue is one known trigger for hallucinatory events. But you are wrong to claim people didn’t hallucinate purely imaginary beings. They did that all the time: hallucinations of angels, archangels, demons, Satan, pagan gods and demigods, and long-dead prophets and sages were so common in antiquity you could fill volumes with the accounts of them.

      Thus, we cannot decide historicity on this detail.

  11. CJO says

    “I think a historical Jesus is the best explanation of the facts, in particular, the fact that people apparently ‘saw’ Jesus after his death.”

    Not a fact. It could be that people, including Paul, ‘saw’ Jesus in scripture originally, and later, after significant literary development, stories came to be written that tell of people apparently ‘seeing’ Jesus after his death.

    I don’t know what it is about this one question (HJ) that seems so readily to allow episodes in stories to become facts in peoples’ minds.

  12. says

    If I had one critique of Proving History it would be that you didn’t really go into how you use Bayes’ Theorem wrong. Like going into things like the Base Rate Fallacy or Dutch Booking. The latter you did explain a bit, but I don’t recall offhand if you explained which probabilities besides the hypothesis and the alternative need to add up to 1.00 or why you’re shooting yourself in the foot if you Dutch Book yourself.

    I skimmed McGrath’s review/follow ups in the comments and his critiques of your position on the historical Jesus (even though it’s off topic for this book) lean towards base rate fallacies. The conditional probability that his hypothesis is true makes more sense of some particular evidence than the alternative, while subtly ignoring the prior probability. Basically pointing out that P(E | H) is high for some class of evidence and then concluding that P(H | E) is the same; not realizing that you’re supposed to use Bayes over and over again to continually update the prior. I also got the same sort of vibe from the critiques of using Bayes over at R. J. Hoffmann’s blog.

    I’m sure this point will be made more explicit in your next book about the historical Jesus, but it could be something to look into if you revise Proving History.

    • says

      In the book I mention the problem you are talking about in general, and that users of Bayes’ Theorem need to study the ways people can err in probabilistic reasoning generally (see pp. 65-66). But I don’t mention specific fallacies, no.

      If you know of a good one-stop-shop website that lists and links to discussions of several kinds of fallacies like this, please post it in comments on my blog seeking useful web materials for Bayesians.

      For example, Wikipedia’s lists of cognitive biases and logical fallacies. Dutch Book isn’t on either list, though, and understanding how it can occur in Bayesian reasoning would indeed be useful thing to see, if anyone has already written about it online.

      However, as to the priors needing to sum to 1, though I don’t name the fallacy (of failing at that) as you do, I discuss the matter a lot, on pp. 69-71 (with related warnings on pp. 79-81), including when dealing with more than two competing hypotheses (p. 69). The risk of Dutch Booking in consequents relates to failing to consider P(~e|h), which I discuss specifically on pp. 255-56 (with related warnings on pp. 72-73 and 77-79). My extensive discussion of deriving priors from reference classes is also pertinent (pp. 229-556).

      On your last point, I’m interested in hearing more about that. What exactly do you mean? That they argue the likelihood ratio for a specific item of evidence supports their position, and then conclude they are right (while ignoring both the role of priors and the likelihood ratios for other items of evidence, which can change the conclusion)?

      If so, IMO that would only really be true (in my final analysis) for one single item of evidence: the mention of James being a “brother of the Lord” in Galatians (if we are as generous to historicity as can be). Everything else produces no ratio favoring historicity (most produce a wash, i.e. both theories explain the evidence equally well; and many favor myth, even if only slightly).

      I have always assumed that they assume historicity has a high prior, which IMO is an error of choosing the wrong reference class (they are treating a celestial demigod as being in the same class as any other mundane historical actor), but that that is a mistake has to be proven (and I do that in my next book). Otherwise, I think their most common error is simply not assigning correct likelihoods (what I call “consequents”), because they aren’t informing themselves on what the mythicist thesis and arguments actually are and thus aren’t taking seriously its explanatory power. Which would not be an error in Bayesian reasoning, but an error in assigning premises.

      So if you think they are frequently committing a more formal mistake (of misusing Bayesian reasoning), and not just mis-assigning premises, I’m interested to hear more about that, since I agree that may be something I have to attend to more.

  13. stuart says

    I’m not saying that people don’t have visions of imaginary beings. I’m saying that if Jesus was an imaginary being then we don’t have an understanding of how the visions started, whereas we do have such an understanding if we assume historicity.

    • says

      Visions like that happened constantly to lots of sects (read the Book of Daniel, for example; or the Ascension of Isaiah). So we don’t need any further understanding regarding why a fanatical sect would have them (or have them of celestial beings like archangels and lords). I assume what you mean is that the peculiar content of this vision (regarding a messianic archangel undergoing a salvific sacrifice) requires explanation–but no more than why a dying historical Jesus would inspire such a weird idea, when the more readily available trope was that he was a martyr and righteous man who would be rewarded in heaven and in the future resurrection. Why his death became a necessary atonement for sins (Hebrews 9) is no more explicable on historicity than on myth. It’s simply an ideological innovation that solves a lot of problems facing Jewish theologians at the time…regardless of historicity. I agree this must be discussed. And I will address this a lot in my next book. I have already discussed it somewhat in my Rapture Day talk, although that was historicist (but the same thinking underlying that model, could just as easily have driven a spiritual revelation model); and I have discussed possible inspirations in my Dying Messiah Redux.

    • F says

      As if we are dealing with a factual eyewitness account of completely non-fictional characters: They can hallucinate anything they want (or the author wants), just like real people.

  14. says

    I have a book recommendation. I’ve just started reading Thinking and Reasoning: An Introduction to the Psychology of Reason, Judgment and Decision Making, by Ken Manktelow. I’m only in chapter 1, but he has the clearest and simplest explanation I’ve seen so far of Bayesian probability in that chapter. He also discusses the relative merits of the Kahneman & Tversky research program versus that of Gigerenzer et al., as well as the contributions of others such as Tooby and Cosmides. Of particular note is the method for presenting normalized relative frequencies as a way of aiding comprehension of Bayesian probabilities. This is similar to what Yudkowsky does on his site but easier to understand.

    I hope that helps.

    Richard Martin

  15. noen says

    Further spanking

    An Introduction to Probability Theory and Why Bayes’s Theorem is Unhelpful in History

    Retreat and denialism doesn’t serve you well. Demanding that people comment on your blog before you’ll engage with them does you little good either.

    If you actually care about facts and history then you’d pursue it to the best of your ability regardless of where it took you and whether or not your own personal ox gets gored.

    There are two paths open before you. One leads you to historical accuracy at the cost of your pet theory. The other is your eventual humiliation and loss of professional stature when the Baysian rug gets pulled out from under you.

    It’s your choice.

    But I already know which path you will choose. You will choose humiliation and professional obscurity over honor and integrity. Why? Because you’ve become too emotionally invested in your beliefs.

    Good luck in your future endeavors.

    • says

      It’s a time management thing. I simply don’t have the time to pour through every comments thread about my work. There are literally hundreds of those. But a well-written blog itself, that I will look at. Later this week or next.

      As for your attitude, it doesn’t suggest you are a very reasonable person. Which is yet another reason not to care about anything you recommend I read. You don’t seem capable of grasping the merit of arguments, even those against me.

    • noen says

      My “attitude” as you call it, is different towards different people depending on whether I think they merit a more positive outlook. Your authoritarian treatment of those you disagree with, your inability to talk calmly and respectfully, your full throated embrace of hate, ridicule and slurs as tactic you think are acceptable, all these things within the space of a couple of posts when I first stared reading your blog… they tell me you are not worth investing in a better “attitude” with.

      Your central thesis is gone. Baysian reasoning is not applicable to history in the way you would like to apply it. Mythicism is a fringe historical theory held by cranks and crackpots. You are not going to escape this from unraveling because reality, how things actually are, is not susceptible to your bullying the way people are.

      It is YOUR attitude, that you can bully facts the way you bully people, that needs to change. My prediction is that change will not happen because like all bullies you’re an intellectual coward. It takes courage and humility to admit one is wrong and you have neither of those traits. In fact, like all authoritarians you see them as weaknesses not strengths.

      Even better is that my saying these things will only cause you to push back against them causing you to move further to the fringes which is exactly what I want you to do. I don’t have to worry about revealing my intent because I don’t think you’re able to rise above your small minded petty squabbles, your admiration of ridicule and slurs. Good luck with that.

    • corkscrew says

      Richard: The same guy has written a follow-up here. You might want to start with it – it’s IMO more informative and less nit-picky.

      Key bit:

      So the obvious question is: if we want to know P(H|E), what shall we use to calculate it? Either of the two formulae above need us to calculate P(E), in the universe of possible histories, how likely are we to have ended up with the evidence we have? Can we calculate that?

      And here things start to get tricky. I’ve never seen any credible way of doing so. What would it mean to find the probability of the New Testament, say?

      Even once we’ve done that, we’d only be justified in using Bayes’s Theorem if our calculations for P(H) and P(E|H) are much more accurate than we could manage for P(H∩E). Is that true?

      I’m a maths grad myself, and I must say my instinctive response is the same (although I have not yet had the opportunity to read Proving History). Bayes’ theorem is very effective in its raw form: a simple mathematical statement that allows us to update well-defined probability distributions with newly-acquired numerical data. That’s how we use it in actuarial work at my company.

      I am extremely suspicious of its use in other contexts, where hard numbers are not available. It may be useful leverage for digging out people’s implicit assumptions, but it isn’t actually necessary for this (as you proved in your Ignatian Vexation post). So I’m not sure what value it adds, beyond lending the enterprise an air of truthiness.

    • says

      I don’t think you know what “authoritarian” means. And you obviously have not spent much time following my work or my engagement with critics. Your resort to hasty generalization is exactly the kind of thing I’m talking about. Your judgment is not sound. It’s guided by emotionalism and hyperbole.

      And what’s more, this still has nothing whatever to do with whether the Jesus myth theory has merit, or Bayesian reasoning should govern historical conclusions. That you think it does is really the nail in the coffin here. You are simply not a reasonable person.

    • says

      I answer those questions in Proving History. I have quite a lot to say about it there (in fact arguably half the book is about answering that), so if he is not responding to any of it, his critique is useless.

    • malcolms says

      “What would it mean to find the probability of the New Testament, say?”

      The way that Dr. Carrier uses Bayes’s theorem avoids these sorts of difficulties. This is because he is usually conditioning all the terms in the numerator and denominator on a more general event, such as “religious books like NT,” and then ends up with priors like “how often in general are protagonists in religious texts like the NT mythical?” rather than “what is the a priori probability that Jesus didn’t exist?” Of course, this then makes the prior itself a conditional probability, which could either itself be computed by another application of Bayes’s formula or else by a direct frequency calculation.

  16. sawells says

    I love the idea that “Bayes’ theorem is not useful in history”. After all, why on earth would anyone studying history need a method which tells them how to correctly adjust their opinions in response to evidence?

    • WAIRH says

      You’ve gone off the deep end, noen. You aren’t even making any sense now, though it’s quite a show for the people reading you.

      “How does a myth get married?”


    • DrVanNostrand says

      The fragment you quote is from something like the 4th century. There are dozens of wildly contradictory gospels from the 4th century or earlier.

      How does a real person do so many wildly contradictory things?

      Answer: He doesn’t. Your thesis is bollocks.

      Obviously, this kind of simple-minded “reasoning” isn’t helpful in determining historicity. You’re just trolling at this point.

  17. malcolms says

    As someone who has read and understood both your book and Ian’s review and also has a background in mathematics, I’ll take it upon myself to explain his criticisms (with some comments of my own) so that you can respond to them:

    He has written 2 posts on your book so far, with a promised 3rd to come. His 1st post starts out by stating:
    “I will be unable to deal with every mathematical problem in the book in a short review, so will limit myself to issues arising from the first mathematical chapter [Chapter 3].”

    1. Your form of Bayes’s theorem is “confusing and unnecessarily complex.” His preferred form of BT is P(H|E) = P(E|H)P(H)/P(E).

    He has 2 objections to your form of the formula: (1) The denominator has been expanded, which he feels is unnecessary. [I pointed out to him that most textbooks actually state BT with the expanded denominator and that most applications of the theorem that one encounters use it in that form as well, but he replied that in his own field (AI) he only needs P(E), so maybe this is just his personal preference from his own experience. Moreover, you give both forms of BT in the appendix.]

    (2) Adding the background explicitly is “highly idiosyncratic,” “condescending,” and “irksome,” reminiscent of William Lane Craig. [I agree that it is unusual and unnecessary, but it is not wrong, as even he acknowledges. Moreover, it is easier to transition to the form of the equation that you actually are using, whereby some of the evidence is incorporated into the background, but you never make this explicit.]

    2. He also criticizes you for failing to explain the derivation of BT or discussing the definition of conditional probability generally: “While Carrier devotes a lot of ink to describing the terms of his long-form BT, he nowhere attempts to describe what Bayes’s Theorem is doing. Why are we dividing probabilities? What does his long denominator represent?” Consequently BT becomes “a kind a magic black box.”

    He then states cryptically: “In this Carrier allows himself to sidestep the question whether these necessarily true conclusions are meaningful in a particular domain. A discussion both awkward for his approach, and one surely that would have been more conspicuously missing if he’d have described why BT is the way it is.”

    [I'm not sure what point Ian is making here, but I think he is alluding to the difficulty of calculating P(E), which he discusses in his 2nd post. As I'll point out later, his criticism is based on a misunderstanding of how you are applying BT.]

    3. His next criticism is one that I partially share: “Carrier correctly states that he is allowed to divide content between evidence and background knowledge any way he chooses, provided he is consistent. But then fails to do so throughout the book.” He cites as an example, p. 51, where the prior is defined to explicitly include evidence in it. [The prior should be the probability that the hypothesis is true before any consideration of the evidence.] He continues with this quote from your book [which I also find objectionable]: “For example, if someone claims they were struck by lightening five times … the prior probabilty they are telling the truth is not the probability of being struck by lightening five times, but the probability that someone in general who claims such a thing would be telling the truth.”

    This is his response: “This is not wrong, per se, but highly bizarre. One can certainly bundle the claim and the event like that, but if you do so Bayes’s Theorem cannot be used to calculate the probability that the claim is true based on that evidence. The quote is valid, but highly misleading in a book which is seeking to examine the historicity of documentary claims.”

    Ian’s point is that BT is defined as P(H|E) = P(E|H)P(H)/P(E), with the prior by definition being P(H), i.e., without any conditioning on the evidence. In the example of the claim of being struck by lightning 5 times, the hypothesis H would normally be “someone was struck by lightning 5 times” and the evidence E would be “he claims to have been struck by lightning 5 times.” Then the prior would indeed be the probability of being struck by lightning 5 times. You instead have as your prior the conditional probability that someone is telling the truth when he claims “in general such a thing,” which would be (part of) the evidence for the claim.

    [Effectively what you are doing is treating the evidence E ("someone claims to have been struck by lightning 5 times") as if it were an intersection of E with a larger set, F ("someone claims such a thing"), that is more general, and then absorbing F into B. The form of BT that you are using is then:
    P(H|EB) = P(E|HFB)P(H|FB)/P(E|FB).

    Now, this trick may be useful for actually calculating P(H|BE), since then you avoid having to calculate P(H|B) or P(E|B), but you haven't been entirely upfront with the reader about what you are doing.] Moreover, as he points out in the quote above, you still are left with P(H|FB), which is very similar to P(H|EB), so you haven’t really used BT to solve the problem.

    [In the actual applications in your book, what you generally do is use BT in this way to reduce the problem to conditional probabilities with more general evidence, and then use an empirical frequency to estimate them. This avoids the problem that he raises about having to estimate, say, the probability of the NT existing.]

    To be continued….

    • says

      Thanks. This is helpful.

      (1) and (2) are pedantic and belie an ignorance of pedagogical principles and therefore are not really a worthwhile criticism. For example, a humanities major is not going to understand what P(E) is or how it derives from the sum of all probabilities; they are also going to have a much easier time estimating P(E|H) and P(E|~H) because estimating those probabilities is something they have already been doing their whole lives–they just didn’t know that that’s what they are doing. Much of my book is about pointing this out. This is also why I keep B in all terms (as I even explain in an endnote), so that laymen won’t lose sight of its role at every stage. And why I don’t bore or waste the reader’s time by explaining how BT was derived or proved; instead, I refer interested readers to the literature that does that. That’s how progress works: you don’t repeat, but build on existing work. I don’t have to prove BT or explain how it was derived; that’s already been done. I just have to show how BT can be applied to my field (history).

      (3) likewise ignores the fact that historians need to do different things than scientists. Thus the way I demarcate B from E is what is most useful to historians (again, I even explain this explicitly in an endnote). Historians are testing two competing hypotheses: that a claim is true vs. the claim is fabricated (or in error etc.), but to a historian that means the actual hypotheses being tested are “the event happened vs. a mistake/fabrication happened,” which gives us the causal model “the claim exists because event happened vs. the claim exists because a mistake/fabrication happened”; and B contains the background evidence relating to context (who is making this claim, where, to what end, what kind of claim is it, etc.), which gives us a reference class that gives us a ratio of how often such claims turn out to be true usually, vs. fabricated (etc.). You then introduce additional indicators that distinguish this claim from those others, to update your priors. And you can do that anywhere in the chain of indicators (so you can start with a really general reference class, or a really narrow one–and which you should prefer depends on the best data you have for building a prior, which historians rarely have any control over, so they need more flexibility in deciding that).

      You could, if you wanted, build out the whole bayesian chain (e.g. see endnote 11, page 301), all the way from raw data, but why should historians trouble themselves with that? They already have context-determined estimates of the global reliability of statements based on their experience. If they get into an argument over conflicting estimates there, then they can dig into the underlying assumptions and build out the whole bayesian case from raw data (or at least from further down the chain of underlying assumptions). But it’s a massively inefficient waste of their time to ask them to do that all the time, or even a lot of the time.

      Ultimately, all bayesian arguments start in the middle somewhere. If they didn’t, they’d all have priors of 0.5 (or whatever ramifies equally the spread of all possible hypotheses). Ian might prefer to start somewhere past the assembly of raw sensory data and toward the frequency-sets of basic event-occurrences (so he would try to answer the question “did Winston Churchill exist?” by starting with questions like “what is the physical probability that a man named Winston Churchill would be born in time to be Prime Minister of England during WWII?,” which would be a ridiculous way to proceed), but even that is doing what I am doing (he is skipping a step: in this case, how we know the frequency data about names is correct, given a certain body of sensations Ian experiences). Historians usually skip all the science steps. Because they’re doing history. Not science (in the narrow sense). But one can always go back in and check those steps. If you had to for some reason.

      In short, historians need to be more flexible in how they model questions in Bayes’ Theorem. Ian’s pedantry wouldn’t help them at all. Because it really doesn’t matter how you build the model. As long as you can articulate what you are doing, and it’s correct (as I explain in chapter six, especially). Because then it can be vetted and critiqued. Which is all we want. And that is all my book arms the historian to do. And that’s all she needs to get started.

      Indeed, having these conversations (about what models to use and what frequencies fall out of them, and thus how to define H and demarcate E from B) is precisely what historians need to be doing. My book gives them the starting point for doing that. Because otherwise it won’t be the same for every question, because the data-availability differs for each case and thus historians have to demarcate differently in different cases.

    • malcolms says

      Part 2.

      So far all of his criticisms have been stylistic (either about how equations were expressed or how there were explained), rather than truly mathematical. The rest of his post is no different.

      4. He takes you to task for using Bayes’s formula as a synonym for Bayesian reasoning. In particular, he ridicules this quote from your book: “any historical reasoning that cannot be validly described by Bayes’s Theorem is itself invalid.” His objection seems to be that, while BT is of course true, there are other equations that one could derive from the definition of conditional probability that couldn’t be derived from BT.

      [Actually, one could derive the formula for conditional probability from BT if one had some sort of definition of conditional probability that implied P(AB|B) = P(A|B) and P(A|AB) = 1: If one assumes BT (i.e., P(H|E) = P(E|H)P(H)/P(E)) then P(H|E) = P(HE|E) = P(E|EH)P(HE)/P(E) = P(HE)/P(E). But this is besides the point, since you only limited your claim to "historical reasoning," a term which you unfortunately didn't define.]

      He further states your attempt to prove this “laughable” assertion is not credible, but gives no other reason than what I just stated above.

      5. He then goes on to discuss your “cheeky” proposal to unify frequentist and Bayesian interpretations of probability. His criticisms here are that your proposal is “unnuanced” and presented as if were original, when it is not. (Not that he is accusing you of taking credit for others’ ideas but rather of being possibly unaware of previous work in the field.) He also states that this “hubris” is typical of “a tone of arrogance and condescension that I consistently perceived throughout the book.”

      6. As a final comment on the mathematics he raises 2 issues but doesn’t elaborate on either: “I felt there were severe errors with his arguments a fortiori…and his set-theoretic treatment of reference classes was likewise muddled (though in the latter case it coincidentally did not seem to result in incorrect conclusions).” This is the entire extent of his discussion of these, from his perspective, problems.

      [I'll more to say about a fortiori reasoning in my next posted comment.]

      7. In his conclusion he has some positive things to say about the book:
      “Outside the chapters on the mathematics, I enjoyed the book, and found it entertaining to consider some of the historical content in mathematical terms….History and biblical criticism would be better if historians had a better understanding of probability….

      I am also rather sympathetic to many of Carrier’s opinions, and therefore predisposed towards his conclusions. So while I consistently despaired of his claims to have shown his results mathematically, I agree with some of the conclusions, and I think that gestalts in favour of those conclusions can be supported by probability theory.”

      But here is his final critique:
      “But ultimately I think the book is disingenuous. It doesn’t read as a mathematical treatment of the subject, and I can’t help but think that Carrier is using Bayes’s Theorem in much the same way that apologists such as William Lane Craig use it: to give their arguments a veneer of scientific rigour that they hope cannot be challenged by their generally more math-phobic peers.”

      As you can see, he hasn’t presented any concrete objection to the mathematics in the book – just the way the mathematics was presented and explained and the overall tone of the book.

    • says

      (4) remains unintelligible to me. It seems like a total non sequitur. If he doesn’t deal with the formal deductive argument at all (pp. 106-14), it’s useless as a critique. Indeed, that is the point of formalizing the argument: so critics would be able to identify any errors that invalidate the conclusion. If he’s not even going to do that…?

      (5) is just ad hominem. I am sure I don’t know all the arguments published on this point (it must be in the thousands, counting books and articles), and if anyone has articulated the same conclusion before, I’d love to accumulate those references (so if he provides them, please copy them here). That is neither here nor there. Whether he dislikes my tone or thinks it’s arrogant or condescending is not a valid rebuttal to whether it is correct. I also don’t think it’s an objective assessment, since I am responding to the debate as framed in recent literature by leading professors of mathematics (some of which I actually cite in the book), so he is actually critiquing them for not knowing the solution I propose. After all, if they don’t know about this unoriginal argument of mine (and if they did, they’d have resolved the debate with it in the literature I cite), then why is it condescending to suggest it to them?

      (6) I’ll certainly concede that my colloquial discourse will lead to ambiguities that chafe mathematicians; but this is precisely the kind of shit they need to get over, because they are simply not going to be able to communicate with the humanities if they don’t learn how to strategically use ambiguity to increase the intelligibility of the concepts they want to relate. It’s like Heisenberg’s Uncertainty Principle: you can have precision with unintelligibility to almost everyone but extremely erudite specialists, or you can have ambiguity with intelligibility to everyone else. The more ambiguity, the greater the clarity, but the lower the precision. This is really a fundamental principle of all nonfiction literature, and a basic principle of science popularization. I have a particular audience. I am writing for them.

      (7) the difference between me and Craig is revealed by all of Ian’s qualifying remarks (like “coincidentally did not seem to result in incorrect conclusions,” a backhanded way to admit I’m actually using it correctly, unlike Craig, thus negating his analogy). As you know, the whole point of my book is to prevent Craig-style abuses by making it clear how to use it correctly and how to spot its being used incorrectly. And indeed I repeatedly emphasize that anyone who wants to use it needs to be clear in how they are using it so it can be vetted and critiqued, thus avoiding the “dazzling with numbers” tactic by arming the reader with the ability to see through it.

      So, overall, all I see here is an out-of-touch mathematician who doesn’t understand how to communicate math concepts to humanities majors, and thus ironically is grossly condescending to humanities majors (whom I’m actually writing for) in the very effort to accuse me of being condescending to mathematicians (whom I’m not writing for). Not a very useful critique, IMO.

    • malcolms says

      Part 3.

      Now I’ll turn my attention to Ian’s 2nd post: http://irrco.wordpress.com/2012/09/12/probability-theory-introductio/

      Most of his post is taken up with an explanation of conditional probability and Bayes’s theorem, which is actually pretty good; it would’ve been a good idea to devote a few pages in your book to something like this. But so far there’s no criticism of your book, or even really much mention of it. I’ll start the numbering over again from 1 to list his criticisms, which eventual start to appear.

      1. For historical questions, there usually is no easy way to calculate, or even estimate in many cases, P(E). He says, “I’ve never seen any credible way of doing so. What would it mean to find the probability of the New Testament, say?…I’m not sure I can imagine a way of calculating either P(H∩E) or P(E|H) for a historical event. How would we credibly calculate the probability of the New Testament, given the Historical Jesus? Or the probably of having both New Testament and Historical Jesus in some universe of possibilities?”

      [He writes as if he didn't actually read your book, although I know that he has, because he is going by his own knowledge of using Bayes's theorem and not looking at the examples where you apply it. As I pointed out in a previous post, you get around the issue of estimating P(E) and P(H) by conditioning on general statements of the evidence, so that you're calculating P(H|F) and P(E|(~H)&F). These need to be estimated somehow, but may be easier since the evidence F is more commonly encountered. It's funny that he observed you doing this in his first post but then never thought through the implications for the rest of his posts. I suggest that if you explained what you were doing mathematically and how it differed from the way scientists usually state and apply Bayes's theorem there would not be so much confusion.]

      2. He then asks whether using the expanded-denominator version of the formula [which he again annoyingly attributes to you and Craig as if you are the only ones who write it this way, and he's not talking about the inclusion of the background here either] could ameliorate this problem with estimating P(E):
      “This is just a further manipulation. The bottom of this equation is still just P(E), we’ve just come up with a different way to calculate it, one involving more terms. We’d be justified in doing so, only if these terms were obviously easier to calculate, or could be calculated with significantly lower error than P(E).”
      [He doesn't seem to think that P(E|~H) is often easier to calculate than P(E), nor does he notice the advantage of using a variable, P(E|~H), that is independent of the other 2, P(H) and P(E|H), unlike P(E), which isn't. Perhaps if he looked at your examples or even the standard example of medical testing he'd see why the expanded form often works better.]

      3. His next criticism is a bit bizarre, as he complains about having to use estimates:
      “If these terms are estimates, then we’re just using more estimates that we haven’t justified. We’re still having to calculate P(E|H), and now P(E|~H) too. I cannot conceive of a way to do this that isn’t just unredeemable guesswork. And it is telling nobody I’ve seen advocate Bayes’s Theorem in history has actually worked through such a process with anything but estimates.”
      [Of course you use estimates - even in the sciences one does. Unless you're doing a problem with dice or cards, the numbers one plugs in are always estimates. And you present several examples where you attempt to justify your estimates. It would help if he actually addressed one to show why it was nothing but "unredeemable [sic] guesswork.”]

      He sums up in a similar vein:
      “So ultimately we end up with this situation. Bayes’s Theorem is used in these kind of historical debates to feed in random guesses and pretend the output is meaningful.”

      4. As a teaser for what he intends to write about in a later post, he states why he thinks a fortiori reasoning doesn’t work:

      “But, you might say, in Carrier’s book he pretty much admits that numerical values are unreliable, and suggests that we can make broad estimates, erring on the side of caution and do what he calls an a fortiori argument – if a result comes from putting in unrealistically conservative estimates, then that result can only get stronger if we make the estimates more accurate. This isn’t true, unfortunately, but for that, we’ll have to delve into the way these formulas impact errors in the estimates. We can calculate the accuracy of the output, given the accuracy of each input, and it isn’t very helpful for a fortiori reasoning.”

      [His characterization of your a fortiori argument - "if a result comes from putting in unrealistically conservative estimates, then that result can only get stronger if we make the estimates more accurate" - is easily demonstrably true: P(H|E) is monotonically increasing in P(H) and P(E|H) and decreasing in P(E|~H), so it follows immediately that if one takes a maximum estimate for P(H) and P(E|H) and a minimum one for P(E|~H) then the estimate for P(H|E) using Bayes's theorem is a maximum, and similarly one derives a minimum for P(H|E). Furthermore, tightening the possible ranges for these variables yields a tighter range for P(H|E), so the a fortiori argument is in fact valid.

      I think what he is intending to say is that while one may in principle get a possible range for P(H|E) from possible ranges for the other probabilities, in practice, the range turns out to be too wide to be useful. Whether that turns out to be the case will be seen when you actually try to apply it.]

      His final comment supports my reading of him: “It doesn’t take much uncertainty on the input before you loose any plausibility for your output.”

      [If this were true it would true for all uses of BT, so how does he account for its use in science? It's not like those estimates for false positives in DNA testing (in his example) lack errors.]

      5. He hints at another problem here but says he’ll explain some other time:
      “[I]n subjective historical work, sets that seem not to overlap can be imagined to overlap in some situations. This is another problem for historical use of probability theory, but to do it justice we’ll need to talk about philosophical vagueness and how we deal with that in mathematics.”

      6. There are 4 footnotes to the post, only the last of which could be taken as a criticism of using BT with uncertainty (specifically the form of BT with the denominator expanded). Here it is in full:
      “You’ll notice, however, that P(E|H)P(H) is on both the top and the bottom of the fraction now. So it may seem that we’re using the same estimate twice, cutting down the number of things to find. This is only partially helpful, though. If I write a follow up post on errors and accuracy, I’ll show that errors on top and bottom pull in different directions, and so while you have fewer numbers to estimate, any errors in those estimates are compounded.”

      [Since P(E|H)P(H) appears in both the numerator and denominator, an increase in it would increase both the numerator and denominator, so the effects from each would offset, not compound! But P(H) appears in the second term in the denominator, so it is not quite that simple. Changes in P(E|H) would partially cancel in the numerator and denominator, making P(H|E) less sensitive to changes in it, but for P(H) depending on the ratio of P(E|H) and P(E|~H), the effect of changes in the prior on the top and bottom of the fraction can indeed compound, but not for the reason he stated.]

      That is his whole criticism. Basically he doubts that BT can be practically used in BT because he feels the inputs are too subjective and have uncertainties that are too wide. We’ll have to wait for your next book to see if you can pull it off.

    • says

      Again, I greatly appreciate your summaries and responses. This took a lot of time and thought, a big help to me. So I owe you a drink if ever we meet.

      (1) You are right, I’m actually articulating ways to get around the very problem he’s talking about (which I certainly acknowledge: note, for example, my discussion of it on pp. 110-14). Where we can’t, we can’t claim to know anything (Axiom 3, page 23; also Axiom 5, page 28). His question how we derive “the probability of the New Testament” is unclear (what exactly does he mean?), but I address something quite close to it on pp. 77-79, using GMark rather than the whole NT (and I get even more specific in my discussion of emulation criteria: pp. 192ff.). If he ignores that, then he is not critiquing my book, but some straw man of it.

      In any event, the problem is addressed by (a) being less ambitious in what you will attempt to prove (a lesson historians often need to learn anyway) and (b) being more clear and precise in laying out what evidence it is that you think produces a differential in the consequents (most evidence simply will not, and therefore can be ignored). Thus “the whole NT” is irrelevant to historicity; likewise even “the exact content of Mark.” We will need to get much more specific than that (What is it in Mark that makes any significant difference? And why? We can model your answer using BT). And in my next book I do that.

      Ironically, he is committing the very fallacy here that I warn against in the book: if we cannot estimate P(E|H), then historical knowledge is simply impossible. Because all historical conclusions implicitly rely on estimates of P(E|H) (and/or P(E|~H)). All historical conclusions ever reached before now, and all that will ever be reached by anyone ever. Thus, if BT can’t solve this problem, no method can. And if he thinks otherwise, it’s his task to produce that method, a method by which (a) a historian can get a conclusion about history without (b) ever relying on any implicit assumption about any P(E|H) or P(E|~H). Good luck with that. Because it can’t be done. If he’d tried it, he’d know.

      (2) You have already effectively rebutted this point. He’s just unable to grasp the way BT has to be employed in the humanities, and what it takes to translate how people in the humanities already reason, into terms definable within BT.

      (3) You have already effectively rebutted this point, too. He seems to be conflating “not knowing x precisely” with “not knowing x at all.” I explicitly address this fallacy several times in the book (early in chapter six, and in my discussion of arguing a fortiori: pp. 85ff.). In short, historians don’t need the kind of precision Ian seems to want. In fact, as I explain in the book, that they can’t get it even if they wanted it is precisely what demarcates history from science: pp. 45-49.

      (4) You have already effectively rebutted this point as well. Like you say, we’ll have to see what he comes up with (do let me know). But I suspect he is ignoring everything I explained in the book about the fact that historians have to live with some measure of ambiguity and uncertainty far beyond what scientists deal with; that’s what makes it different from science (again: pp. 45-49; and again, Axioms 3 and 5). He seems to either want history to be physics, or he seems to think I want history to be physics. The one is foolish; the other betrays a failure to really read my book (e.g. pp. 60-67).

      (5) As you note, his criticism here is too vague to even know what he means. At present no response is required.

      (6) doesn’t seem mathematically informed, unless he means errors in P(E|H) and P(E|~H) can pull in different directions; otherwise, P(H) and P(~H) always sum to 1, so they actually consist of a single estimate, not two, so they can’t pull against each other. If you estimate P(H) against yourself, you have also estimated P(~H) against yourself, by definition. And if you do the same with both P(E|H) and P(E|~H), they can’t ever pull in opposite directions, either. The compounded error between them will then only make your argument more a fortiori. So there isn’t any discernible criticism here.

      So far I am not impressed. It doesn’t look like he’s taking any argument in the book seriously. It’s almost like some Cato Institute effort at refuting a policy that they don’t really have any valid argument against but they have to refute it anyway so they come up with whatever trivia and handwaving they can think of.

Leave a Reply

Your email address will not be published. Required fields are marked *

You may use these HTML tags and attributes: <a href="" title=""> <abbr title=""> <acronym title=""> <b> <blockquote cite=""> <cite> <code> <del datetime=""> <em> <i> <q cite=""> <strike> <strong>