Mythicist Math

Mythicist Math July 9, 2018

Richard Carrier has taken to calling me a doofus and launching a variety of other insults in my direction. And so presumably I’ve highlighted an important problem with his stance, since otherwise there would be no need for a lengthy screed that deals in insults rather than substance, as is par for the course with Carrier, and which (as is also typical for Carrier) misrepresents what I wrote from the very outset.

You’ll notice, if you read his post, that he immediately depicts the situation as though I had said that probability in the realm of history is non-mathematical, or had suggested that there is something inherently problematic with Bayesian reasoning. Those who read my blog post, of course, will know that what I criticized was what Carrier does with Bayes’ Theorem and the mathematics of historical probability. If someone were to use Bayesian logic without plugging in the specious claims and problematic interpretations that Carrier offers time and time again, they might well draw conclusions that are reasonable.

The irony, of course, is that (as again is so typical) Carrier resorts to claiming that I must not have read his books, while seeming not to have read my brief blog post that he is supposedly responding to, at least not carefully or with any level of serious interest in hearing what I was saying and responding to it substantively.

Anyone who wishes to determine whether I’ve read Carrier’s books can read the reviews, articles, and blog posts I’ve written and compare them to Carrier’s books’ contents in detail. I trust that they will find that the problems that I identify are genuinely there!

Carrier’s blog post offers precisely the kind of argument I criticized in my recent blog post as well as in others before that: the idea that it is somehow relevant to historical assessment what the odds are that a random name drawn out of a hat of all names will denote someone purely mythological or purely historical (as though those were the only two options). But even within Carrier’s own Bayesian approach, his conclusions are still unpersuasive. He says towards the end of his post that if I would only put Jesus in the correct reference class, it would all become clear. His proposed reference class is that of mythical figures as defined by the Rank-Ranglan scale, which is dubious for numerous reasons laid out in one of my several review articles about Carrier’s book On The Historicity of Jesus. I am confident that if Carrier were to use a more obvious and appropriate reference class, such as that of Jewish messianic and prophetic figures from around the time of Jesus, the calculations would turn out differently. If he were to recognize that the Gospels cannot simply be dealt with en masse but must be evaluated in terms of their specific contents, then he might also get something resembling a valid result.

But the point remains: if we have an authentic letter from someone who met an individual’s brother, and we judge that individual’s historicity probable on that basis, the addition of spurious information does not diminish the likelihood that the letter-writer met the brother of that individual and thus was in a position to know whether they were historical or not. If everything else they learned about that individual was pure fabrication, it would diminish the historical accuracy of their portrait of him, but it would not diminish the likelihood of the individual’s historicity.

I’m not going to repeat the points I have made before about the problems with detail after detail in Carrier’s argument (such as when he treats the common name Joshua/Jesus as though it were a too-convenient name for a savior god – begging the question by casting Jesus as a god and not a human being as Davidic anointed ones were expected to be). Let ms simply conclude by quoting what Carrier says on p.337 of his book that I supposedly have not read: “Obviously, if Jesus Christ had a brother, then Jesus Christ existed.”

 

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  • John MacDonald

    All Jesus scoring high on the Rank Raglan scale may imply is simply that there was some legendary embellishment of Jesus’ biography patterned after some hero that scored high on the scale, such as Oedipus (21 or 22 points), Theseus (20 points), or Romulus (18 points). Dennis MacDonald has done a lot of work on how the Jesus narrative imitates the Greeks, and MacDonald is convinced Jesus was historical. And, folklorist Alan Dundes noted that Raglan himself had admitted that his choice of 22 incidents, as opposed to any other number of incidents, was arbitrarily chosen.

    • John MacDonald

      One other thought: I think Dr. Mcgrath has admirably illustrated the principle flaw in Dr. Carrier’s method. Carrier writes:

      “History Is Mathematical. All statements of probability are mathematical.” see https://www.richardcarrier.info/archives/14352

      But McGrath points out:

      “If someone were to use Bayesian logic without plugging in the specious claims and problematic interpretations that Carrier offers time and time again, they might well draw conclusions that are reasonable.” see http://www.patheos.com/blogs/religionprof/2018/07/mythicist-math.html

      So, historical assessments involve not only “Quantitative Probability,” but also “Qualitative Interpretations” that produce the “Quantitative Data” to be inputted into Bayes’ Theorem.. Not only “Quantitative Analysis,” but also “Qualitative Analysis” can be plotted on a continuum between zero and one. For instance, we can plot a professor’s proficiency in grammar as being close to one “Quantitatively” (e.g., by saying she “ALWAYS” uses correct grammar), or “Qualitatively (e.g., by saying she “EXPERTLY” use the rules of grammar). But this doesn’t make “Qualitative Judgments” mathematical. And this is true of other disciplines. For instance, in my background as a public school teacher preparing a report card, “ADVERB MODIFIERS” such as (a) QUANTIFIERS (e.g., “usually,” “sometimes,” etc) and (b) QUALIFIERS (e.g., “proficiently,” “competently,” etc) both can explain the letter grade in the comment section of the report card, even though the former are mathematical while the latter are not – both can, for instance, be used to describe student performance and what a letter grade means on an elementary school report card.

      Dr. McGrath’s point seems to be not so much about Carrier’s Quantitative Judgments, but rather the Qualitative Interpretive Judgments Carrier is making that inform/produce the data that Carrier is plugging in to Bayes’ Theorem. The interpretations Carrier is making of the evidence are problematic, so the quantitative data he is producing with these interpretations and then plugging into Bayes Theorem are resulting in an un-objective, biased result that reflect the a priori mythicist point of view Carrier operates from.

  • Tom

    You rock. Keep rocking….

  • Mark

    I tried for once to comment on his site and got the response that I sounded like a bot and was then banned. I guess I should have known better.

    I made the point that, on the subjective interpretations of probability – which he needs since it is the only extant interpretation that assigns probabilities to singular propositions – the only clear inputs for conditional probabilities are about the likelihood of a sample having a certain character, on the hypothesis of a given underlying distribution or frequency. In theory even this is subjective ‘prejudice’ – maybe I think God is messing with /my/ sampling of coin flips – but it’s a little too obvious that the thing to say is, e.g. ‘P (all three samples are heads | the flips are distributed evenly) = 1/8’ . The ‘obviousness’ of these conditional probabilities is what gives force to the Bayesian inference backward to ‘P(the flips are distributed evenly, i.e. the coin is fair | all three samples are heads)’ , which of course requires other subjectively provided material.

    None of this structure is present in ‘P (Paul does’t describe the Nativity | Jesus existed)’; the former isn’t a sample of the latter; there isn’t a long run of the former; the latter isn’t a general remark about a distribution or frequency.

    The whole labor of the great theorists of this interpretation like De Finetti and Savage was to show stuff like this: that, though updating requires a prior ‘prejudice’ about e.g. the frequency of heads and tails in coin flips, still over a long run of samples this subjective element will disappear; that the order of sampling is irrelevant; etc etc. Given this fact, and the fact that we have ‘obvious’ conditional probabilities about sampling, we get good statistical inference about an unknown distribution by the Bayes rule turnaround. Carrier informs me that he has proven such results himself. I can’t tell if he’s stealing the credit from De Finetti , Savage et al. He seems to think I hadn’t already mentioned his supposed results in my remark.

    He then draws the absurd conclusion that the results show something like this: there is no distinction between subjective interpretations of probability and objective, frequentist, interpretations. This is not the way to put it, but even if it were, it could only apply where the propositions in which I have a subjective confidence level can be recast as frequencies. In the ‘frequentist’ or ‘objectivist’ statement ‘P(E1 | E2) = x’, E1 and E2 are ‘events’ that can recur, not historical propositions. But, as I had, Carrier pretty much only has singular historical propositions so he must be a radical subjectivist about the procedure.

    It’s true that on the subjectivist reading of the questions ‘P (Paul does’t describe a Nativity | Jesus never existed)’ , ‘P (Paul mentions a crucifixion | Jesus never existed)’ , I am supposed to have an answer. But I am quite blurry about it, in fact; by contrast, my view of the corresponding ‘P (all three samples are heads | the flips are distributed evenly)’ is absolutely clear. The Paul question is just another thing about which I must be coherent, not a principle I can use for inference.

    • Jim

      Ty for your insightful comment and framing “the math” in perspective. Contrary to his denials, Carrier typically conflates his Bayesian analysis with frequentist inference when he makes his assertions. I suppose that it’s easier to write a blog rant accusing others (and ban people who have logical perspectives), than to sit down and work things through (especially when you have an agenda that isn’t linked to contributing to knowledge).

  • If everything else the letter writer learned about the individual in question was pure fabrication, I think that might give us some grounds to question whether he was in a position to know who the individual’s siblings were.

    • Not necessarily. Imagine for instance someone embarrassed by the fact that their sibling is in prison, and who thus claims they are in the military, concocting story after story about their battles. Not only do those fabricated stories not make the sibling’s existence less factual, but it may be that embarrassment about a real sibling is the only or most plausible explanation for the fabrication in the first place. Misrepresentation of a real individual and invention of a purely fictitious one are very different phenomena.

      • They are very different phenomena, but the question is what conclusion I am justified in drawing based on the fabricated stories.

        It is perfectly plausible for someone to have a sibling, and I think it reasonable to accept a person’s claim to having one. On the other hand, if none of the stories that the person tells about his sibling is plausible, that would open me to the possibility that the sibling himself is fictitious. Misrepresentation due to embarrassment is certainly a plausible explanation for the fabrications, and I might even conclude that it was the more likely than the complete invention of the sibling; nevertheless, I cannot imagine that I would consider the existence of the sibling an established fact without independent corroboration.

        • You may or may not know that the stories are fabricated, at least not initially. When you find out, it will not change the historicity of the sibling, and may only make sense in light of the existence of the sibling.

          • Nothing will change the historicity of the sibling–he either exists or he doesn’t. The question is whether the evidence makes it reasonable to conclude that he probably existed.

            There might well be other reasons to conclude that the sibling existed despite the fabrication of the stories. In that case, however, the fabricators claims might carry very little weight.

        • John MacDonald

          In Hesiod’s “Works and Days,” some scholars, like classicist E.L. Bowies, suggest Hesiod invented the claim that he had a brother Perses (see Bowie, “Lies, Fiction and Slander in Early Greek Poetry,” 23).

          • It would be really interesting to do a comparison between that case and that of James and the brothers of the Lord, looking at how similar or different the evidence is, how similar or different the judgments of historians are, what arguments and reasons are offered, and so on. Could be illuminating, couldn’t it?

          • John MacDonald

            Two thoughts:

            (1) There is dispute among classicists as to whether Hesiod had the brother Perses he talks about. “Works and Days” provides a lot of biographical information about Hesiod. He includes details about a quarrel he had with Perses over his father’s land. Some classicists like Martin West think that Perses was a real person and that some details were invented for the purpose of argument. Those like Bowie think it’s just as likely Perses was invented. Importantly, Bowie comments that “In a poem communicating apparently sincere views on the gods, justice, and society, as well as practical, if traditional, information on methods of farming, the didactic poet did not think he would weaken the authority he so clearly arrogates by incorporating biographical details about his addressee which members of his audience would detect as fictitious (Bowie, 23).”

            (2) There is an ever-growing library of desperate mythicist intellectual contortions to try to explain away the plain reading of the James passage in Galatians: (a) Price offers that it might be a nickname, like a Chinese ruler who was called “the little brother of Jesus.” (b) Carrier offer it is a cultic title for non apostolic baptized Christians. This leaves the rather odd sounding consequence that Cephas would not be a brother of the lord. (c) Neil Godfrey at Vridar has an entire library of articles trying to discredit the usual reading of the James passage in Galatians (see https://vridar.org/category/new-testament/brother-of-the-lord/ ). Godfrey comments that “There are indeed reasonable grounds for doubting that that verse was known to anyone before the third century. There are also reasons to doubt that anyone had any idea that James, a brother of the Lord, was indeed a leader of the Jerusalem church until the third century. There are good reasons to suspect the passage was introduced to serve the interests of an emerging ‘orthodoxy’ against certain ‘heresies’ ( See https://vridar.org/2018/07/11/that-one-piece-of-solid-evidence-that-weighs-strongly-in-favour-of-historicity/ ).”

            To me, all the mythicist special pleading on this issue seems like the Catholic apologetic attempt to get around the idea that Jesus had a brother named James because it conflicts with their bias about the perpetual virginity of Mary.

          • John MacDonald

            I had another thought regarding Carrier’s approach to the James passage in Galatians. As I said, Carrier interprets “brother of the lord” to be a cultic title, not a biological one, to refer to all non apostolic baptized Christians. Carrier has to make this “non apostolic” distinction because the Galatians passage distinguishes James from the apostle Cephas, James being a brother of the lord, while Cephas is not. But Carrier’s cultic interpretation here excluding Cephas from being a brother of the lord seems to contradict Romans 8:29, which says Jesus is the first born of many bretheren – implying Cephas would indeed be a brother of the lord in a cultic sense. I think the evidence is very strong in favor of a biological interpretation of “brother of the lord” with the James passage in Galatians.

          • John MacDonald

            I actually had a fun conversation with Carrier about this. The conversation went:

            JM: Romans 8:29 seems to suggest all Christians were brothers of the lord, not just non apostolic baptized Christians.

            RC: Of course. But just as you’d say “I met the Pope and a Christian named James,” you’d say “I met the Apostle and a Christian named James.” In no way do these statements mean the Pope or Apostle is not a Christian too. Rather, they mean the other is just a Christian, without rank.

            JM: Does it really make sense to say Paul spent 15 days with Cephas and the only non ranking Christian he met was James? What about Cephas’ family? It would make sense if Paul was saying the only other apostle he met was James.

            – As Ehrman points out, the distinction between Cephas and James is not that one is an apostle and the other is just a regular Christian, but that both are apostles and one is Jesus’ brother, while the other is not.

  • John MacDonald

    I’m a bit of a philosophy nerd, so I get excited when we start to define the grundbegriffe for whatever topic we are discussing. In historical analysis, the term “probable,” while certainly involving “the qualitative (as Dr. McGrath showed in challenging Carrier’s interpretations that Carrier is using to generate his numbers),” seems to have a mostly quantitative sense. To say something “probably happened” suggests 0.51 or greater, while to say something “probably didn’t happen” suggests 0.49 or lower. Some try to avoid the quantitative sense of “probable” by suggesting the alternative of an apparently more qualitative term like “plausible” as the basic concept. The problem is that “plausible” is usually defined as “reasonable or probable.” On the one hand, historians aren’t really interested in simply making a “reasonable” hypothesis, because many competing models could be equally “reasonable.” Rather, historians want to know what “likely” did or did not happen. Similarly, if we are defining “plausible” with the concept “probable,” this simply brings the quantitative back as the focus. But conversely, the quantitative also “folds back” onto the the qualitative. For instance, if we propose a continuum of probability between 0 (impossible) and 1 (certain), we may have a progression of modifiers such as: impossible – highly unlikely – very unlikely – unlikely – somewhat doubtful – merely possible – somewhat likely – likely – very likely -highly likely – certain. These modifiers are not just abstract ranges of quantity, but at one point in time were grounded in real qualitative appeals to our own lives. For instance, a child doesn’t learn the meaning of the word “likely” simply by appealing to math, but rather by being given real concrete examples of “likely” from their own lives (e.g., it is “likely” their mother will return home from work around 5 pm because that is what “usually” happens). The question of the quantitative is, at the same time, the question of the qualitative, while the question of the qualitative is, at the same time, the question of the quantitative.

  • ydoethur

    I would add that another very significant problem with Carrier’s methodology is that even if mathematical formulae were suitable for these kind of projects – which they are clearly not – he doesn’t have the necessary training or skill to apply them properly. I could go into more detail but I think you will find all you need to know about Carrier’s shortcomings here:

    https://letterstonature.wordpress.com/2016/02/05/final-word-on-richard-carrier/

    Dr Luke Barnes is a cosmologist at the University of Sydney who uses Bayesian techniques in his work – most recently published by Cambridge University Press.

    The key point to bear in mind is that while Carrier has training in using Bayes, he has none at all in the philosophical underpinnings of it. His training was a few days’ work in 1991 in how to handle sonar equipment. He has clearly, given his very basic confusion between frequency and plausibility, made no effort to gain the necessary knowledge.

    And then, even if we accepted his weird and wonderful new interpretation of the mathematics, we’re still left with the awkward fact he falsified evidence (e.g. as Gullota so ably demonstrated, rewriting the Rank Raglan index to fit Jesus) in order to support his theories.

    It remains a source of puzzlement to me that people take this figure in any way seriously.