Richard Carrier’s ”On the historicity of Jesus” A Review From a Bayesian Perspective Tim Hendrix∗ April 22, 2016
Contents 1 Introduction
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2 How Bayes’ theorem is applied in On the Historicity of 2.1 Definition of the hypothesis of historicity h . . . . . . . . 2.2 The evidence: . . . . . . . . . . . . . . . . . . . . . . . . . 2.3 The computation . . . . . . . . . . . . . . . . . . . . . . .
Jesus . . . . . . . . . . . .
5 6 8 9
3 Proving or guessing history: Bayes’ theorem and errors 3.1 The gameshow . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2 How Bayes’ theorem inflates errors . . . . . . . . . . . . . . . . . 3.3 The effect of systematic bias . . . . . . . . . . . . . . . . . . . . . 3.4 An example using errors estimated from On the Historicity of Jesus 3.5 But doesn’t the upper and lower bounds fix this? . . . . . . . . .
10 10 11 13 15 16
4 Examining the logic of On the Historicity of Jesus 4.1 The trial-example: Why accuracy matters . . . . . . . . 4.2 The hypothesis of Myth and historicity . . . . . . . . . . 4.2.1 Bobs defence has a new strategy . . . . . . . . . 4.2.2 Conflating background information and evidence
17 18 20 24 25
5 Prior bamboozlement 5.1 The Rank-Raglan prior of historicity . . . 5.1.1 Jesus almost certainly didn’t exist accounts says he does . . . . . . . 5.1.2 A close reading of the Gospels . . 5.2 What reference classes can’t do . . . . . . 5.2.1 Adding properties . . . . . . . . . 5.3 Bobs lawyer computes a prior . . . . . . .
. . . . . because . . . . . . . . . . . . . . . . . . . . . . . . .
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∗ Tim Hendrix is not my real name. For family reasons I prefer not to have my name associated with my religious views online. This is the third revision of this manuscript.
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5.4
5.5
The Rank-Raglan prior examined . . . . . . . . . . . . . . . . . . 5.4.1 The response to the alternative reference class objection examined . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.4.2 First “proof” Jesus existed, the written account reference class . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.4.3 Second “proof” Jesus existed, the Josepheus reference class Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.5.1 So what is the true prior? . . . . . . . . . . . . . . . . . .
33 34 36 37 40 41
6 Other comments 42 6.1 Not using Bayes’ theorem . . . . . . . . . . . . . . . . . . . . . . 43 6.2 What Paul really meant . . . . . . . . . . . . . . . . . . . . . . . 44 7 Discussion 7.1 Bayes’ theorem and history . . . . . . . . . . . . . . . . . . . . . 7.2 Summarizing the counter-argument to On the Historicity of Jesus 7.3 Final comments on On the Historicity of Jesus and Proving History
48 49 49 51
Appendices
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A Bayes’ theorem
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1
Introduction
Dr. Richard Carrier’s recent book, On the historicity of Jesus, (Sheffield Phoenix Press, ISBN 978-1-909697-35-5), is the second of two volumes in which Dr. Carrier investigates the question if Jesus existed or not. In this and the first volume, Proving History, Dr. Carrier argues that the current state of Jesus studies has failed to recover the true Jesus because they have relied upon developing historical criteria to determine which parts of a text can be trusted or not. According to Dr. Carrier all criteria and their use is flawed. Rather, in the two volumes Dr. Carrier suggests we should only rely on Bayesian arguments: The first step in that process was to assess the methods so far employed on the subject and replace them if faulty. I accomplished that in the previous volume, in which I demonstrated that the most recent method of using ’historicity criteria’ in the study of Jesus has been either logically invalid or factually incorrect, and that only arguments structured according to Bayes’s Theorem have any chance of being valid and sound. Here I apply that method to the evidence for Jesus and show what results. (On the Historicity of Jesus, preface) As indicated by the quote, this second volume examines the evidence for and against the existence of Jesus using Bayes’ theorem. The outcome of a Bayesian argument is a probability that Jesus existed or not. In other words, the answer to
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the question is a number between 0 and 1 such that 1 implies we are absolutely certain Jesus was historical, 0 implies we are absolutely certain Jesus was not historical and for instance 0.75 (or 75%) implies we are somewhat convinced Jesus was historical. The main contributions of On the Historicity of Jesus is: In other words, in my estimation the odds Jesus existed are less than 1 in 12 000. Which to a historian is for all practical purposes a probability of zero. For comparison, your lifetime probability of being struck by lightning is around 1 in 10 000. That Jesus existed is even less likely than that. Consequently, I am reasonably certain there was no historical Jesus. Nevertheless, as my estimates might be too critical (even though I don’t believe they are), I’m willing to entertain the possibility that the probability is better than that. But to account for that possibility, when I entertain the most generous estimates possible, I find I cannot by any stretch of the imagination believe the probability Jesus existed is better than 1 in 3 (On the Historicity of Jesus p. 600) This conclusion is also stated as follows: And yet that is using the absurdly generous estimates concluding every chapter, and especially the last chapter on the Epistles, the only place I could claim to find any credible evidence for a historical Jesus. So 1 in 3 is only the maximum possible probability Jesus existed, meaning we can say with confidence that the probability Jesus existed is in fact less than 1 in 3. (On the Historicity of Jesus p. 599) Or to spell these out, using “absurdly generous” estimates Dr. Carrier arrives at a probability of 31 Jesus existed and using realistic estimates the chance he existed is 0.00008. As mentioned, the method employed to arrive at this conclusion is a Bayesian argument. Dr. Carrier explains it as follows: To know whether any theory is the most probably true, you must compare it with all other viable theories (no theory can be defended in isolation). To effect such a comparison you must establish four premises: (1) the prior probability that the theory you are testing is true, (2) the converse of which is the prior probability that some other theory is true instead, and then (3) the consequent probability that we would have all the evidence we actually have if your theory is true, and (4) the consequent probability that we would have all that same evidence if some other theory is true instead. From these four premises a conclusion follows with logical necessity, which is simply the probability that your theory is true. (On the Historicity of Jesus p. 16) These four items dictates the organization of the books. To provide an overview the chapters are organized as follows: 3
Chapter 1: Surveys what constitutes relevant evidence. Dr. Carrier concludes the relevant evidence can be divided into four categories: (i) extrabiblical evidence, (ii) acts, (iii) the gospels and (iiii) the epistles. Chapter 2 and 3: Formulating sensible, minimal, hypothesis for early christianity on the assumptions Jesus did exist or did not exist. Chapters 4 and 5: Surveying the background knowledge Chapter 6: Estimating how likely the two minimal historical hypothesis are a-priori. Chapter 7-11: Estimate how likely the four categories of evidence is given the two theories (that is, if Jesus existed or did not exist). Chapter 12: The outcome of the two proceeding steps are probabilities. These are then combined using Bayes’ theorem to produce the probabilities discussed in the two quotes. As can be seen from the outline, Bayes’ theorem plays a central role in Dr. Carrier’s argument and appears critical in terms of arriving at the conclusion that “I find I cannot by any stretch of the imagination believe the probability Jesus existed is better than 1 in 3”. Several reviewers on Amazon also points out that the use of Bayes’ theorem to historical questions is an important feature of the book. A representative sample: • First he takes bold strides to change the failed paradigm in historical method, then he applies a superior method (Bayes’ Theorem) and gives us a masterpiece of staggering proportions. (Neumann) • He [Dr. Carrier ] argues for using Bayesian probability in the study of history, especially Jesus. This methodology is breath of fresh air in Jesus studies - instead of ad hoc or even apologetic arguments, Carrier has a method that is based on probability and not just possibilities and wishful thinking. (Quentin D. Jones) • This is Carrier’s best book and hands down the best book on Jesus historicity. Anyone who has trouble with Bayesian arguments will have to admit Carrier uses them surgically and ends up showing convincingly that they give reason a clear windshield for cruising difficult highways. (James Branscome) In this review I will try to examine the Bayesian content of Dr. Carriers argument from the main-stream view of what constitutes valid and invalid application of Bayesian reasoning, a view I have some familiarity with through my education (I have a PhD in Bayesian methods) and my work (a research position with focus on Bayesian methods).
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I have elsewhere discussed Dr. Carriers first volume in the series, Proving History 1 . In that review I believe I identified several areas where Dr. Carriers arguments were lacking, as for instance Dr. Carriers particular non-Bayesian interpretation of probabilities. However a difficulty in writing the review was that Proving History does not provide worked-out examples for how Bayes’ theorem should be applied in practice to solve historical questions such as the existence of Jesus. With an example now being provided in On the Historicity of Jesus I hope to be able to continue the discussion of Bayes’ theorem and it’s application to history and perhaps this will be useful for other historians who wish to assess the applicability of Bayes’ theorem to historical questions. It is important to stress that no matter the validity of Dr. Carriers arguments, a person who desires to look for errors in On the Historicity of Jesus could properly dig up something such as an imprecise use of words (probability and density might be confused). I won’t care for such minor issues in this review, rather I will focus on what I consider to be the most interesting question, how Dr. Carrier will apply Bayesian methods to the question of Jesus existence and thereby arrive at concrete, useful results. I will therefore only raise issues pertinent to core aspects of Dr. Carriers argument which in other circumstances would cause me to go back to the drawing board or give me serious pause regarding the trustworthiness of my conclusions. In other words, I will try to answer the question: Are the results obtained in On the Historicity of Jesus as trustworthy as the above quotes indicates?. A reader should be aware I will limit myself to the Bayesian (logical) structure of the argument and not discuss the many pieces of historical evidence Dr. Carrier presents and interprets. However before we can address Dr. Carriers argument it is important to understand what it is and I will summarize Dr. Carriers argument in the next section. This review assumes familiarity with basic probability theory and a brief review of the notation used is included as an appendix.
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How Bayes’ theorem is applied in On the Historicity of Jesus
It is important to distinguish between two ways to apply Bayes’ theorem to history: The qualitative way: In which one considers a historical argument (or type of argument) and tries to translate the available information into propositions such that the argument can be formulated in the language of probabilities. This might allow us to say something about which probabilities must be very high/low for the argument to work, or why a particular type of argument works. I call this way of using Bayes’ theorem qualitative 1 My review of Proving History can be found at: https://www.scribd.com/doc/271358647/ Richard-Carrier-Proving-History-Review
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because it involves examining an existing argument symbolically but not the computation of exact probabilities. The quantitative way: In which one attempts to derive/estimate a quantitative value of a particular hypothesis by plugging numbers into a Bayesian formula. The qualitative application of Bayes’ theorem is in my opinion unproblematic simply because it is only an aid for reasoning: if it works for you, by all means use it!. The use of Bayes’ theorem in this way is in many ways scientific common sense. For instance, it asks us to formulate our hypothesis and evidence carefully and exactly, to think about what is probable rather than what is possible or absolutely true/false, and to let our judgement be guided by a tradeoff of how a-priory likely our hypothesis is versus how well the evidence is explained by our hypothesis. A book that I believe is representative of this view is Aviezer Tuckers Our Knowledge of the Past: A Philosophy of Historiography [Tucker, 2004]. In my own experience, for some problems, thinking this way can be a help, but for most problems it is not and adding an extra layers of A’s, h’s and P ’s to a problematic argument can sometimes hide rather banal errors. However Dr. Carriers application of Bayes’ theorem is quantitative as it revolves around computing actual probabilities. The basic idea by Dr. Carrier is to apply Bayes’ theorem to history: P (h|E.b) =
P (E|h.b)P (h|b) P (E|h.b)P (h|b) + P (E|¬h.b)P (¬h|b)
here h is the hypothesis in question (Jesus existed), E is the relevant evidence, the dot denotes “and” (for instance h.E is “h and E”), b is our background historical evidence and ¬h is the negation of h, i.e. that Jesus was not historical. In the next sections I will briefly sketch what the various symbols mean for later reference:
2.1
Definition of the hypothesis of historicity h
The hypothesis h and ¬h were discussed already in Proving History. Dr. Carrier writes: In Proving History I demonstrated that we can parcel out the entire prior probability-space to just four classes of hypothesis altogether: • h = ’Jesus was a historical person mythicized’ • ¬h = ’Jesus was a mythical person historicized’ • h0 = ’Jesus was a historical person not mythicized’ (triumphal) • ¬h0 = ’Jesus was a mythical person not historicized’ (postmodern)
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As I argued there, the latter two classes of hypothesis, even collectively. consume a vanishingly small piece of the prior-probabilityspace (certainly less than a one in a million share). They can therefore be ignored. That leaves us with bare historicism and bare mythicism [h and ¬h]. However, both must be more developed than this, not only to make our job easier by ruling out all implausible variations of them, but also to leave us with hypotheses that make more substantial predictions. This will give us in each case a minimal theory, one that does not entail any ambitious or questionable claims (thus keeping its prior probability relatively high), but still leaves us with a theory substantial enough to test (thus keeping its consequent probability relatively high as well). The minimal Jesus myth theory I will develop in the next chapter. Here I will develop the minimal theory of historicity. (On the Historicity of Jesus p. 30) After a discussion of what should and should not be contained in such a minimal theory we arrive at the following list: This gets us down to just three minimal facts on which historicity rests: • An actual man at some point named Jesus acquired followers in life who continued as an identifiable movement after his death. • This is the same Jesus who was claimed by some of his followers to have been executed by the Jewish or Roman authorities. • This is the same Jesus some of whose followers soon began worshiping as a living god (or demigod). That all three propositions are true shall be my minimal theory of historicity. (On the Historicity of Jesus p. 34) Similarly, in chapter 3, minimal mythesism ¬h is fleshed out: • At the origin of Christianity, Jesus Christ was thought to be a celestial deity much like any other. • Like many other celestial deities, this Jesus ’communicated’ with his subjects only through dreams, visions and other forms of divine inspiration (such as prophecy, past and present). • Like some other celestial deities, this Jesus was originally believed to have endured an ordeal of incarnation, death, burial and resurrection in a supernatural realm. • As for many other celestial deities, an allegorical story of this same Jesus was then composed and told within the sacred community, which placed him on earth, in history, as a divine man, with an earthly family, companions, and enemies, complete with deeds and sayings, and an earthly depiction of his ordeals. 7
• Subsequent communities of worshipers believed (or at least taught) that this invented sacred story was real (and either not allegorical or only ’additionally’ allegorical) That all five propositions are true shall be my minimal Jesus myth theory. (On the Historicity of Jesus p. 53) That is, h and ¬h are being considered equivalent to these two lists of propositions.
2.2
The evidence:
The evidence, E in Bayes’ theorem, considered by Dr. Carrier is divided into the following four categories: Gospels: The content of the Gospels Acts: The content of Acts Epistles: The content Epistles Extrabiblical: Extrabiblical evidence (various references to Jesus such as Josepheus) Each of these categories are broken up into subcategories to be treated in seperate sections. For instance the extrabiblical evidence Extrabiblicalis broken up into a number of subcategories the first four of which are: e1 : Twin traditions e2 : Documentary silence e3 : 1 Clement e4 : Ignatius and Ascension of Isaiah .. . in total there are 25 such pieces of evidence e1 , . . . , e25 . Thus in our notation the evidence is treated as: E = Gospels and Acts and Epistles and Extrabiblical = e1 and e2 and · · · and e25 = e1 .e2 . · · · .e25 The background information Next there is the background information which I will only mention briefly. The background information b consists of two long and very informative chapter of various political, religions and social circumstances relating to early christianity.
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2.3
The computation
On the Historicity of Jesus does not state in any single place which formula is used for computing the probability of historicity, however it is reasonably easy to re-construct it from the available information. First, notice that according to Bayes’ theorem: P (h|E.b) =
P (E|h.b)P (h|b) P (E|h.b)P (h|b) + P (E|¬h.b)P (¬h|b)
(1)
it follows: P (h|E.b) P (E|h.b)P (h|b) = P (¬h|E.b) P (E|¬h.b)P (¬h|b) Then Dr. Carrier assumes that P (E|h.b) = P (e1 .e2 . · · · e25 |h.b) = P (e1 |h.b)P (e2 |h.b) · · · P (e25 |h.b) (and similar for ¬h). If we plug this into the above equation we obtain: P (e1 |h.b) P (e2 |h.b) P (e25 |h.b) P (h|b) P (h|E.b) = × × ··· × × P (¬h|E.b) P (e1 |¬h.b) P (e2 |¬h.b) P (e25 |¬h.b) P (¬h|b) This is sometimes known as the odds ratio. What we are of course interested in is not (directly) the odds ratio but the actual probability Jesus is historical (h|E.b) P (h|E.b). However if we obtain a value of the above ration, r = PP(¬h|E.b) , then we can easily convert that back into a probability of Jesus being historical because P (h|E.b) =
1 1+
1 r
1
= 1+
P (e1 |¬h.b) P (e1 |h.b)
× ··· ×
P (e25 |¬h.b) P (e25 |h.b)
×
P (¬h|b) P (h|b)
(2)
This is quite a mouthful, however the upshot is that according to Dr. Carrier, in order to compute the probability Jesus is historical P (h|E.b), all we need to estimate is the prior probability P (h|b) and the 25 ratios: P (e1 |¬h.b) , P (e1 |h.b)
P (e1 |¬h.b) P (e25 |¬h.b) ,··· , P (e1 |h.b) P (e25 |h.b)
In practical terms, Dr. Carrier use historical considerations to estimate the prior probability P (h|b) and the probabilities of each piece of evidence given historicity h and non-historicity ¬h and this discussion takes up the bulk of the text. To give a feeling of what these numbers are Dr. Carrier estimates that P (¬h|b) ≈ 0.0625 and then, letting ri = PP(e(err|¬h.b) |h.b) , r1 = 0.6
r2 = 0.4
r3 = 1
r7 = 1
r8 = 0.5
r9 = 0.4
r13 = 1
r14 = 0.5
r19 = 1
r20 = 1
r4 = 1
r5 = 0.5
r6 = 1
r10 = 0.5
r11 = 1
r12 = 0.5
r15 = 0.5
r16 = 1
r17 = 0.8
r18 = 1
r21 = 1
r22 = 1
r23 = 1
r24 = 1
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and r25 = 1. All of these numbers are then combined to produce the final probability P (h|E.b). This is done with two sets of numbers, corresponding to Dr. Carriers realistic estimate as well as his most generous estimate, and this produces the two estimates of the probability Jesus existed of P (h|E.b) ≈ 0.3233 ≈ 31 and P (h|E.b) = 12 1000 . The next sections will consider the various steps of this argument more carefully.
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Proving or guessing history: Bayes’ theorem and errors
I everything that can be said about the applicability of Bayes’ theorem to history should be seen in light of the observation Bayes’ theorem inflates errors. It is therefore worth spending some time examining this problem with a simpler toy example.
3.1
The gameshow
Forget everything about probabilities and history and suppose you are at a gameshow where there is a table with the following items on top of it: • An apple • A teddy bear • A box of crayons and your goal is to guess the weight of the apple, mA , as accurately as possible. You can do this in one of two ways: (i) you make your best guess as the weight of the apple or (ii) you make guesses at the weight of the teddy bear mB , crayons mC and the total weight mT of all three items and then compute the weight of the apple as: mA = mT − mB − mC . I think everyone will recognize the second strategy is both suboptimal and rather silly. Why? A person who wished to defend the formula could point out things in it’s favor, for instance that it is a proven mathematical fact or that it may be difficult to guess the weight of the apple and the formula avoids this difficulty2 . These are however obviously poor arguments: The problem with the formula is that the estimates of mT , mB , mC on the right-hand side each come with an error, and when you subtract or add two numbers to each other the (relative) error in the difference will be larger than the individual errors. The formula thus inflates the error in mA . For instance, it is possible that we estimate the total weight to be lower than the sum of the weight of the two other objects (remember we make these estimates individually) and in that case the formula will tell us the weight of the apple is negative. 2 These observations more or less parallels the arguments presented in Proving History in favor of using Bayes’ theorem.
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Guessed weight of apple, method 2 True weight of apple (112g)
Chance of guessing at this weight
Chance of guessing at this weight
Guessed weight of apple, method 1 True weight of apple (112g)
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Figure 1: Suppose our ability to guess the weight of the apple mA has an error given by the distribution in the left-hand pane, i.e. we typically guess within about 15g of the true weight of 112g. If we assume this error is representative of our ability to guess the various weights when estimating mA = mT − mB − mC , then using this formula magnifies the error with about a factor of 1.7 shown in the right-hand pane. Secondly, while the use of the formula seemingly has the advantage of no longer requiring us to guess the weight of the apple, we still have to guess weights, namely the weight of the two other objects as well as their total weight and therefore the formula is predicated on the assumption that we can indeed guess weights accurately. However, if we make this assumption, then we can also pursue strategy (i) and just guess the weight of the apple, and we would no longer have the problem of the error being inflated due to the substraction. In other words, the second strategy invites us to make incoherent assumptions. Of course there are cases where the formula will work. For instance, if we were told the total mass and the other objects had masses which were easy to guess (for instance bottles of soda). However a person who wished to advocate strategy (ii) over strategy (i) would have to argue this is indeed the case since strategy (ii), as outlined above, is inherently more prone to errors than strategy (i). It will not do to say: “Well, strategy (i) is hard, so I suggest we use strategy (ii)” since strategy (ii) is inherently more difficult to apply than strategy (i).
3.2
How Bayes’ theorem inflates errors
Bayes’ theorem magnifies errors the same way strategy (ii) did in the example with the apple. This should be apparent by simply inspecting the expression eq. (1), however it is worth providing some quantitative guidance to how large this effect is. If we first focus on the example with the apple and we suppose our
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Probability of historicity True value p(h|E)=0.3233
Chance of guessing at this value of p(ei |h)
Chance of guessing at this value of p(h|E)
Value of factor True value of p(ei |h)
0
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Guessed value of each factor p(ei |h)
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Probability of historicity p(h|E)
Figure 2: Similar to the apple-example in fig. 1, suppose our ability to guess the probability of each factor in the Bayes computation P (ei |h.b) has an error as given in the left-hand pane, then using Dr. Carriers formula will magnify this error by a factor of 5 to produce the error in the probability Jesus existed, P (h|E.b), shown in the right-hand pane. ability to guess the weight will be off by a random factor as illustrated in fig. 1 in the left pane. In the figure, the blue line illustrates the chance of guessing a particular weight of the apple and according to the figure the chance of guessing more than 150g or less than 80g is neglige. If we assume an uncertainty of the same magnitude affects our ability to guess the weight of the other two items and the true weight, then the uncertainty in our ability to guess the weight by the second method is as illustrated with the red line in the right pane; as we can expect, the error is inflated by a factor of roughly 1.7, and we now often make unrealistically high or low guesses of mA . The same concept applies for the guesses at the various probabilities in the Baysian computation eq. (2). If we assume our ability to guess each factor P (ei |h.b) in the computation is off by just a small amount as seen in fig. 2 (left pane), the errors in the various factors will combine (just as it was the case for the apple example) to induce a nearly uninformative distribution of our estimate of historicity, P (h|E), shown in the right-pane.3 Notice the width of this distribution is much larger than was the case in the left pane (in fact it is about 5 times wider), and this is despite an assumption we are fairly good at guessing the true probabilities (shown in the left pane). The bottom line is this: • Bayes’ theorem, as used by Dr. Carrier, will magnify the errors by a factor 5 (approximately). • (equivalently) To estimate the probability of historicity at a given precision 3 For
illustrations sake I use the upper-bound supplies by Dr. Carrier
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using the method of Dr. Carrier it must be assumed all other probability estimates can be made with 5 times higher precision. In the following I will try to illustrate the consequences of this effect in two ways. The first is by examining the effect of systematic bias (that is, being slightly too optimistic or pessimistic regarding the evidence) and the second is by estimating the magnitude of the error (the width of the blue curve in fig. 2, left pane) from Dr. Carriers numbers and examine what that error implies for the probability of historicity.
3.3
The effect of systematic bias
Humans are not perfectly rational but come with inherent biases for or against various ideas. Accordingly, it is reasonable to consider how well Bayes’ theorem will function when applied by a human operator who is at least slighly biased. To this end, we consider Alice and Bob. Alice is ever so slightly biased for historicity and she overestimates the probabilities of the evidences on historicity and correspondingly underestimate the probability on mythicism by a few percent. Bob is biased in the same manner but towards mythicism. For instance suppose the “true” value of the evidence of “Ignatius and Ascension of Isaiah” is P (Ignatius and Ascension of Isaiah|h) = 0.061, P (Ignatius and Ascension of Isaiah|¬h) = 0.079 Then if Alice is 4 percent biased she would estimate: PAlice (Ignatius and Ascension of Isaiah|h) = 0.061 × (1 + 0.04) = 0.0634, PAlice (Ignatius and Ascension of Isaiah|¬h) = 0.079 × (1 − 0.04) = 0.0758 Remember, these probabilities are based on subjective judgements without any way of externally confirming if we are right or wrong and the reader is invited to consider how accurately he or she could estimate “The probability of Acts given historicity” (I would be quite happy if i made it within 20%) The result can be seen in fig. 3. It shows that with no bias (0 percent), Alice and Bob both agree on the probability of historicity of P (h|E) = 0.3233. When the bias increases to only 5%, Alice concludes there is more than 85% chance Jesus is historical and Bob at the same time and considering the same evidence believes there is less than 5% chance Jesus was historical!. For small values of the bias, this spread corresponds to a roughly 20 times increase in uncertainty. I believe a bias of 5%, considering we rely on subjective judgement, is very, very low indeed. Consider for instance the relative bias humans exhibit when judging numerical values such as the age of another person, the price of some good, the rise/fall in unemployment under Regans administration or the relative size of the Chinese economy and keep in mind these are objectively available facts and not guesses of the probabilities of how likely particular ancient manuscripts are given different hypothesis. 13
Probability Jesus is historical, p(h|E)
Biased for historocity (Alice) Biased against historocity (Bob)
1 0.8 0.6 0.4 0.2 0 0
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4
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8
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Bias in percent Figure 3: Effect of systematic bias. Suppose Alice uses Dr. Carriers estimated probabilities but is ever so slightly biased towards historicity in her estimates of the various terms (a bias of 4% means estimating 6.34% rather than 6.1%, see text) and Bob is similarly ever so slightly biased against historicity. The two curves show the effect of the bias on their final judgement of historicity, for instance at 4% bias Alice believes Jesus almost certainly did not exist and Bob is nearly certain he did. Accordingly, we must assume we are absolutely unbiased when estimating probabilities when we apply Dr. Carriers method. Systematic bias has in this section referred to a subjective, irrational bias. It may(?) be objected we should simply ignore this affect because it has to do with psychology, or that no such bias affects Dr. Carriers assignments of probabilities because he has considered the matter very thoroughly and objectively. However, as will be shown in the following sections there are other sources of systematic bias than psychology and in the following sections I will point out simple but subtle ways systematic bias can (and arguably is) introduced. At this point we can conclude: • Dr. Carrier’s use of Bayes’ theorem magnifies bias by around a factor 20 • To use Bayes’ theorem we must assume we (and others) have a fully neglige bias and no other sources of bias exists • Any non-neglige bias will lead to wildly diverging results
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Chance of guessing at this value
Probability of historicity
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1
Probability of historicity p(h|E) with errors estimated from OHOJ
Figure 4: If we estimate the error of the individual terms as being equal to the mean difference between the upper/lower bounds Dr. Carrier supplies in his text this results in an extremely broad, uninformative posterior distribution of historicity.
3.4
An example using errors estimated from On the Historicity of Jesus
I argued previously Dr. Carrier’s use of Bayes’ theorem roughly inflated errors by about a factor 5 provided the errors are fully unbiased. Naturally this raises the question what the value of the errors actually are. After all, if the errors are very small, inflating them by a factor 5 might not be too bad. The bad news is I don’t think there is any objective way to estimate the errors. After all, these are errors in our subjective judgement on how plausible something seems to be. I suppose one could gather a large number of historians and see which values they independently came up with, but this too would not really inform us about the errors but about how well historians agreed with each other. In On the Historicity of Jesus Dr. Carrier provides his estimates of the upper and lower bounds for the relative magnitude of the various terms in the computation, i.e. fractions of the form: P (e1 |h) , P (e1 |¬h)
P (e2 |h) ,··· . P (e2 |¬h)
One way to proceed is to estimate the typical size of the error from these upper and lower bounds. In some cases, Dr. Carrier’s estimate of the upper and lower bounds agree; since I don’t think this is realistic, I will only consider those terms where the upper and lower bounds differ. Doing this I arrived at the plot shown in fig. 4. As can be seen, with errors of this magnitude we can effectively
15
arrive at any value of the probability of historicity P (h|E)4 . My estimates of the errors can naturally be criticized from various perspectives and I certainly do not claim this is the only way of going about the problem. In the main this criticism revolves around the formal vagueness of On the Historicity of Jesus, for instance that Dr. Carrier’s choice of providing upper/lower bounds of various fractions does not correspond to any sensible statistical practice. I will very tentatively conclude: • If the error of the various probabilities is of the magnitude corresponding to the upper/lower bounds this is sufficient to allow nearly any conclusion to be drawn from the data. Mind this is assuming we are fully unbiased in our error estimates. With just the slightest bias, errors of the size estimated here would lead us to conclude whatever our bias predisposed us towards with near certainty.
3.5
But doesn’t the upper and lower bounds fix this?
An objection to what I have discussed above is that since Dr. Carrier provides upper and lower bounds of the various terms, and from these terms compute upper and lower bounds on the probability of historicity, then the probability of historicity is upper and lower bounded and so the conclusion holds regardless of how Bayes’ theorem may inflate errors in other circumstances. There are two principal comments to be made to this type of argument. Firstly, the use of upper and lower bounds do not correspond to any sensible Bayesian procedure. What are the upper and lower bounds supposed to represent? Presumably, at least for the upper bound, is supposed to represent some sort of confidence interval. I.e. we can be 95% sure the “true” probability is lower (or greater) than this bound. The problem with this idea is that the use of confidence intervals in this manner is both wrong and not required. If we do not know what the true weight of the mass of the apple mA is, Bayesianism suggests we should represent that uncertainty with a probability distribution as shown in the left pane of fig. 1. Similarly, if we do not know the exact probability of a given term, for instance x = P (e3 |h.b), then we should represent that uncertainty using a probability density of x as shown in the left pane of fig. 2. It may seem extravagant to consider “a probability of a probability” 5 , however this is done all the time in standard Bayesian analysis. It is in other words completely standard textbook stuff and in fact the only thing we can do if we do not know the probabilities. To consider such an analysis, consider again the term P (e3 |h.b). Recall e3 was the evidence found in “1 Clement”. To say the upper and lower bounds of the ratio r = PP(e(e33|¬h.b) |h.b) are both 1 (as Dr. Carrier does) is to say we have no 4 Since the terms are fractions I work in the log domain. I then compute the mean of the difference between the log of the upper and lower bounds and assumed the error was uniformly distributed within these bounds. This is by no means the only way to go about the problem and the result should only be taken as an illustration. 5 More precisely stated, a probability density of parameter which represents a probability
16
uncertainty in this ratio at all. It is a much stronger statement than to say this ratio has mean 1 or that we do not know what the ratio is; in all these cases we should assign a probability distribution to r which reflects our uncertainty in the value. The problem is that when this is done the errors are inflated dramatically as previously illustrated. This brings us to the second problem. Dr. Carriers arguments in On the Historicity of Jesus relies on particular interpretations of certain passages. Presumably, if these interpretations are different then this would affect the argument somehow, i.e. it induces uncertainty in the estimates of the various probabilities. It is not at all clear if the final probabilities reflect this uncertainty (I will provide examples of this later on in a brief discussion of the Epistles). If there exists a (plausible) textual reading of a certain passage which is true with some non-vanishing probability and much easier explained on historicity than mythicism then this induces uncertainty in the estimated probabilities. Whether one considers upper or lower bounds, or a Bayesian analysis, this induces uncertainty in the estimated probabilities. The upper and lower bounds discussed in On the Historicity of Jesus cannot represent anything but Dr. Carriers particular choices in his interpretation or how these choices on average affects the probabilities. These considerations are perhaps much easier illustrated with the gameshow example. It is possible to postulate for instance an upper bound on the apples weight by saying the total mass must be no higher than some value and the mass of the two other objects can’t be any lower than two other values. However these postulated upper and lower bounds depends on all kinds of things, for instance we might lower bound the mass of the crayons using an assumption crayons has the same density as rock. When all is said and done we can insist the lower bound represents the absolute extreme of our estimates, however we can’t really know. Suppose in a gameshow example that a bias of just 5% in the estimates would be sufficient to throw off the bounds how confident would we really be? It seems unclear why this is any more exact than simply saying an apple can’t weight more than say 300g.
4
Examining the logic of On the Historicity of Jesus
In this section, I will go over the specific argument presented in On the Historicity of Jesus and present the specific reasons why I think Dr. Carrier misapplies Bayes’ theorem in On the Historicity of Jesus. I will show that Dr. Carrier makes (subtle) assumptions and conflations which favors mythicism and which, to be formally correct, requires the prior probability P (h|b) to indicate a very specific event. However as will be shown in the next chapter the prior is (quite trivially) incorrectly computed, rendering the overall argument erroneous. I will use a running example of a trial to illustrate the various moves made in On the Historicity of Jesus and why they are of consequence to the overall argument.
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4.1
The trial-example: Why accuracy matters
Since all probabilities used by Dr. Carrier depends on the definition of historicity h and myth ¬h, the exact definition of these terms is very important and any difficulty in their definition can dramatically affect the entire computation. To give the reader an impression of the kind of difficulties we can easily find ourselves in I will consider an example of a criminal trial where we consider the proposition: g : “Bob is guilty” given different pieces of evidence. Suppose for instance e1 is the evidence that a hair was found at the crime scene which matches Bob according to a DNA test6 . In ordinary Bayesian reasoning we would then have: P (e1 |g.b)P (g|b) P (g|e1 .b) = P (¬g|e1 .b) P (e1 |¬g.b)P (¬g|b) if we suppose we are a-priori uncommitted to Bob being guilty, P (g|b) = P (¬g|b) = 12 , then under the natural assumptions the chance Bobs hair is found at the crimescene is much larger given Bob is guilty than if he is not guilty, P (e1 |g.b) > P (e1 |¬g.b), and we can conclude Bob is likely guilty. For definiteness assume P (e1 |g.b) = 10 000 × P (e1 |¬g.b) in which case P (g|e1 .b) = 99.99% So far so good: If your hair is found on the crime scene and you don’t live there, you are likely guilty of the crime. However in an actual trial both the defence and the prosecutor will argue for a particular theory of what happened. Suppose therefore that the defence argues that Bob is not just innocent, but there was a mixup at the crime lab such that the original hair sample was contaminated with Bobs hair. In other words, suppose the defence introduce as a theory the additional proposition: T : “The hairsample was contaminated with Bobs hair” the defence then argues for the joint proposition (innocence): i = ¬g.T (Or in words: Bob is not guilty and the evidence was contamination). In this case, just as before: P (g|e1 .b) P (e1 |g.b) P (g|b) = × P (i|e1 .b) P (e1 |i.b) P (i|b) However consider the first two terms: If Bob is guilty, then the chance Bobs hair will be found at the crime scene is the chance a criminal will leave hair. However if Bob is innocent and the sample is contaminated, then the chance Bobs hair will be found at the crime scene is just the chance the criminal left 6 we assume Bob does not live at the crime scene and that he has no relationship to the diseased
18
hair, since per assumption the sample would be contaminated so as to match Bobs sample. I.e. P (e1 |g.b) = P (e1 |i.b) and so P (g|e1 .b) P (g|b) = P (i|e1 .b) P (i|b) and so the defence argues Bob should be found innocent since the evidence is indifferent with respect to his guilt and we should be a-priori uncommitted to 1 .b) his guilt (i.e. P (g|b) ≈ P (i|b)) and so PP (g|e (i|e1 .b) ≈ 1 and Bob is not guilty. Should we be convinced by this argument? Not so fast. We now have to account for the term P (i|b). Notice that P (i|b) = P (¬g.T |b) = P (T |¬g.b)P (¬g|b) In general we can conclude that the term P (T |¬g.b) (the chance of contamination given the defendant is guilty) is rather low, in fact for us to reason consistently we can deduce it must be in the order of P (T |¬g.b) ≈ 10 1000 . It it thus this term P (T |¬g.b) which “saves” us from being off by a factor of 10 000. In practice, humans are often very focused on how well hypothesis explains the evidence, i.e. P (e1 |i.b), and not so good at judging the intrinsic probability of a hypothesis P (i|b). This is a common and well-documented flaw in human thinking which we must be aware of. The problem is particulary severe when the addition to the hypothesis (T in this case) has the form of a conspiracy. If the defence proposed the theory that someone had conspired to frame Bob, this would easily explain every piece of incriminating evidence (he was framed see?) while even weak evidence for innocence still counts towards his innocence (the conspirators messed up see?). Consider for instance the idea the Apollo moon landings were faked. Evidence which would normally be considered absolutely conclusive such as video tapes is dismissed as part of the hypothesis (the hypothesis entails the moon landings are faked so video evidence is easily explained as being manufactured), while minor anomalies such as the supposed wind that ripples the flag remains evidence for the conspiracy. In my opinion, this goes a long way to explain why it is so hard to reason people out of conspiracy theories. The bottom line is this: When we add additional elements (what I call theories) to our basic hypothesis, such as contamination in the above example, these will as a rule dramatically alter our assignments of all probabilities since the only reason we propose a particular theory is because it explains the evidence. To counteract this, we must be extremely careful to reason exactly about the prior probability of the theories we propose and correspondingly, we must make very strong assumptions on our ability to gauge the intrinsic prior probability of propositions if the theories are complicated. In the previous case, 1 if the defence inaccurately assumed P (i|g.b) = 100 , their computation would have been off by about a factor of 100. In comparison, in the example with Jesus a factor of 3 is enough to overturn the conclusion of Dr. Carriers conservative estimate. With this in mind, let’s look at how Dr. Carrier defines his hypothesis. 19
4.2
The hypothesis of Myth and historicity
Recall that Dr. Carrier defines his hypothesis of history and myth not simply as whether Jesus existed or not but as theories for his existence. Mythicism ¬h is defined by Dr. Carrier as (introducing mA , . . . , mE ): mA : At the origin of Christianity, Jesus Christ was thought to be a celestial deity much like any other. mB : Like many other celestial deities, this Jesus ’communicated’ with his subjects only through dreams, visions and other forms of divine inspiration (such as prophecy, past and present). mC : Like some other celestial deities, this Jesus was originally believed to have endured an ordeal of incarnation, death, burial and resurrection in a supernatural realm. mD : As for many other celestial deities, an allegorical story of this same Jesus was then composed and told within the sacred community, which placed him on earth, in history, as a divine man, with an earthly family, companions, and enemies, complete with deeds and sayings, and an earthly depiction of his ordeals. mE : Subsequent communities of worshipers believed (or at least taught) that this invented sacred story was real (and either not allegorical or only ’additionally’ allegorical) That all five propositions are true shall be my minimal Jesus myth theory. (On the Historicity of Jesus p. 53) And similarly historicity is defined as a list of four other propositions. If we only focus on mythicism, a difficulty Dr. Carrier does not address in On the Historicity of Jesus is the basic hypothesis of historicity is conflated with a particular theory for historicity and so it is not clear exactly what the basic theory of historicity or mythicism is. I think the closest we come to a definition is the first element of his definition of historicity: “An actual man at some point named Jesus acquired followers in life who continued as an identifiable movement after his death.”. That is, there once lived a man called Jesus who founded a religious group which stands in a causal relationship to christianity today. I will leave the question of what basic historicity and myth exactly is open and simply define bare historicity as the proposition: hB : Jesus was a historical person then ¬hB will be “it is not true Jesus was a historical person”. We can then define mythicism, as it is used in On the Historicity of Jesus, as the conjunction of ¬hB and the five elements of our theory of mythicism: ¬h = mA .mB .mC .mD .mE .¬hB Similar we can introduce the three elements of minimal historicity: 20
This gets us down to just three minimal facts on which historicity rests: h0A An actual man at some point named Jesus acquired followers in life who continued as an identifiable movement after his death. h0B This is the same Jesus who was claimed by some of his followers to have been executed by the Jewish or Roman authorities. h0C This is the same Jesus some of whose followers soon began worshiping as a living god (or demigod). That all three propositions are true shall be my minimal theory of historicity. (On the Historicity of Jesus p. 34) and then in this notation Dr. Carriers definition of historicity is: h = h0A .h0B .h0C .hB . As a preliminary comment, the notation used by On the Historicity of Jesus is simply flawed since quite clearly ¬h is not equal to the negation of h. In other words, Dr. Carrier is not comparing two binary exhaustive propositions and from a technical standpoint the computation used is therefore flawed. This is however not the major issue, the major issue is that adding elements to our theory, just as the case of Bob and the murder trial, can only happen if we are extremely careful to correctly assess the prior probability of the new joint hypothesis, especially when those additional elements are an aid in explaining the evidence. It is no doubt the case that mA , . . . , mE and bare mythicism ¬hB better explains the evidence than just bare mythicism ¬hB . As an example, recall in bare mythicism we start out with only assuming there was no historical Jesus. Suppose then we consider the evidence in the Gospels which obviously describes an earthly Jesus. If we consider the probability of the Gospels given just hB , then creating the Gospels has to involve the Gospel writers somehow making up or coming in contact with an “earthly Jesus” tradition and then decides to write the Gospels as only containing this tradition. On the other hand, if we assume in addition to ¬hB that mE is true,
mE :
Subsequent communities of worshipers believed (or at least taught) that this invented sacred story [Jesus was an earthly man with an earthly family with followers etc.] was real (and either not allegorical or only ’additionally’ allegorical).
Then we are starting from the assumption that the Gospel writer already thought Jesus was a historical person so clearly he would be pre-disposed to write the Gospels about an earthly Jesus. In other words P (Gospels|mE .hB .b) P (Gospels|hB .b)
21
The same goes for other pieces of the evidence: If we assume the Christians already understands Jesus to be historical at the time of them writing their history, the chance of them writing about a historical Jesus is of course much, much higher than if we simply assume the Christians initially start out convinced that Jesus was not historical and had to change their minds within a relatively narrow timescale. Or consider another example:
mB :
Like some other celestial deities, this Jesus was originally believed to have endured an ordeal of incarnation, death, burial and resurrection in a supernatural realm
With an assumption such as this in place, it is of course much much easier to explain certain pieces of evidence. For instance in 1 Thessalonians 2.14 Jesus is said to have been killed by the Jews; however Dr. Carrier regards this to be an interpolation. According to Dr. Carrier, Paul actually believed Jesus to have undergone a heavenly crucifixion by Demons as described in 1 Corinthians 2.8 Thus, when Paul says ’the rulers of this age’ (archonton tou aionos toutou) were the ones kept in the dark and who in result crucified Jesus, he is using archon in its then common supernatural sense: the demonic powers (Element 37). Paul almost never uses this word of earthly authorities, and never so uses it in conjunction with the cosmic vocabulary of aeons. And here he certainly cannot be using it in a human sense, as the motives he is imputing to these archons then make no sense. Rather, this exactly describes what we saw in the earlier redaction of the Ascension of Isaiah: Satan and his demons kill Jesus only because his identity was kept hidden from them, so they wouldn’t know what his death would accomplish (see Chapter 3, 1; with Chapter 8, 6) (On the Historicity of Jesus p. 565) However, if Paul is talking about a crucifixion carried out by demons, this is easily explained if we assume mB , that Paul already believed Jesus to undergone death in the supernatural realm: P (Epistles|mB .¬hB .b) ≈ 1 However if we only believe Jesus was not historical, then Paul talking about a supernatural crucifixion should be compared against any old source mentioning a supernatural crucifixion of any non-historical person, for instance the probability we might have sources discussing a supernatural crucifixion or execution of Robin Hood, Moses or Buddah. In other words again: P (Epistles|mB .¬hB .b) P (Epistles|¬hB .b). So connecting this to the crime-example with Bob, what I have argued so far is that I think it is fair to say the addition of mA , . . . , mE to ¬hB makes it a lot 22
easier for us to explain various pieces of evidence. The elements mA , . . . , mE therefore acts like the contamination hypothesis T in the trial example and accordingly we should be very careful when we assess the prior probability of our joint hypothesis P (mA .mB .mC .mD .mE .¬hB |b). So how does Dr. Carrier do this? Well, according to Dr. Carrier the problem can simply be ignored: (..)technically ¬h (non-historicity) must also include all Jesus myth theories not defined by Premises 1 through 5 [mA , . . . , mE ] (that is, all theories of the evidence for Jesus that entail historicity is false and at least one of Premises 1 through 5 is false), but since their prior probability (even collectively) is surely less than a tenth of one percent (as I just reasoned), and their posterior probability not sufficiently high to make enough of a difference (especially in relation to minimal historicity), these theories share such a small portion of the probability-space occupied by ¬h that they can simply be ignored. In other words, if ¬h (as I have minimally defined it) is false, it’s simply the case that historicity is probably true (On the Historicity of Jesus p. 55) Let’s spell out what this argument must imply. First notice that P (mA .mB .mC .mD .mE .¬hB |b) = P (mA .mB .mC .mD .mE |¬hB .b)P (¬hB |b) So Dr. Carrier argues that, based on a previous argument, P (mA . · · · .mB .hB |b) ≈ P (hB |b). This implies: 1 ≈ P (mA .mB .mC .mD .mE |¬hB .b) The argument Dr. Carrier refers to takes up about one page and itemizes why the background evidence and minimal mythicism implies each of the elements mA , · · · , mE . I will only focus on mE for simplicity. So why is mE entailed by b and bare mythicism ¬hB ? Dr. Carrier explains: Finally, Premise 5 [i.e. m5 ] is already an effective certainty, as it is true even if historicity is true, and is so well verified in background evidence that its prior probability is as near to 100% as makes all odds. So the possibility of its being false will not be an issue. (p. 55) Firstly, that mE is implied by historicity is irrelevant and it is odd Dr. Carrier would bring it up. Secondly, the argument boils down to saying that P (mE |hB .b) ≈ 1 since mE “is so well-verified on background evidence”. But what is this saying? It is saying exactly that assuming our general background knowledge, and assuming Jesus was not historical, we can conclude mE , that subsequent Christians believed Jesus was a real person (or more specifically, that “subsequent stories” about Jesus were true). This is a highly problematic argument: Assume someone is thought not to exist on earth, for instance one of the Gods in the Hindu religion. Then ¬hB 23
is true for this God. However for P (mE |¬hB .b) ≈ 1, then it should be almost certain that subsequent Hindus would place that God on earth with a family, enemies, etc. etc. as implied by mE . Obviously this might happen, but given the many Gods or God-like creatures who start out celestial and remain so presumably it mostly does not happen; similar comments apply for the other properties like that Jesus underwent death and resurrection in the supernatural realm. The only way to “fix” the argument from a formal point of view is to conflate evidence with background knowledge. I.e. we must claim that our background knowledge contains the statement that later Christians (say around year 100) came to believe Jesus was historical. In other words P (mE |¬hB .b) = 1 because our background evidence already contains other facts implying mE . This is actually stated in On the Historicity of Jesus as: Finally, that subsequent Christians believed Jesus was historical [mE ] is an established fact in our background knowledge, and therefore the probability that it is false is virtually zero; and therefore it consumes effectively all the probabilityspace reserved for myth. In other words, any theory of myth that denied this would have an absurdly low prior. It therefore can be ignored as well. (On the Historicity of Jesus p.249) As stated, there is as such nothing illegal in this move from a strictly formal viewpoint, however we have to be extremely careful when arguing some information is part of our background knowledge as we then have to account for how this element affect all terms in our computation. Let’s illustrate this with the trial example. 4.2.1
Bobs defence has a new strategy
Suppose we consider the trial-example with Bob from before and suppose Bobs defence argues that it is part of our background-evidence that Bob was arrested for the crime. The background-evidence is then b = b0 .a0 where a0 is that Bob was arrested. Now recall that e1 was that Bobs DNA was found on the crimescene and T is the theory the DNA-sample was contaminated at the laboratory and i = T.¬g. Where we left off the last time was: P (g|b) P (g|b) P (g|e1 .b) = = P (i|e1 .b) P (i|b) P (T |¬g.b)P (¬g|b) Recall furthermore that what “guaranteed” the right conclusion, that the DNA indicated Bob was guilty, was that the chance of contamination was assumed low on our background knowledge, i.e. P (T |¬g.b) ≈ 10 1000 . However, notice that when we add a0 to the background knowledge Bobs lawyer can make the following (arguably correct) argument: “If Bob is arrested by the police, a0 , this must be because the police think they have found some piece of evidence linking Bob to the crime. Why else make the arrest? But since Bob is assumed
24
innocent, ¬g, and the polices only lead was the hair, there must have been an error incorrectly linking Bob to the crime though the hair and that error must therefore be in the DNA analysis of the hair. So P (T |¬g.a0 .b) ≈ 1 and not very small as the prosecutor claims. Therefore Bob is innocent.”. Notice this argument is true under the assumptions and implies again: P (g|b) P (g|b) P (g|e1 .b) = ≈ ≈ 1(?) P (i|e1 .b) P (T |¬g.b)P (¬g|b) P (¬g|b) So once more we have seemingly acquitted Bob. Of course we can know posthoc this argument is faulty because the DNA must point to Bobs guilt. We can therefore conclude that the inclusion of a0 in b must lower the prior probability of Bob being innocent (or correspondingly increase the prior probability of Bob (g|b) ≈ 10 000 when a0 is included in b. being guilty) by an amount such that PP(¬g|b) I think there are three points worth emphasizing before returning to Dr. Carriers argument: • The first point is that these manipulations is causing our original probability of the evidence (the DNA on the crime-scene) to jump around between the various factors. If we started out with the above computation, i.e. using a0 and T , for us to reason correctly we would have to figure out, without any external guidance or way to check if the argument was sound, that P (g|b) ≈ 10 000P (¬g|b) despite the fact the judge had instructed us originally to be a-priori uncommitted to the clients guilt. • The second point is that correctly reasoning in the above situation requires us to be extremely careful in how exactly we define background evidence, evidence, hypothesis, etc. etc. It also requires us to be extremely careful to preserve and account for this information in subsequent arguments. • The third point is that we cannot simply assume it is innocent to add something to the background evidence because it is generally known or has no causal connection to the hypothesis. For instance, it is generally known Bob is arrested (why else have the trial?) and that him being arrested cannot (backward) cause him to have committed the crime. Still, adding this piece of information, in conjunction with the other assumptions, can easily throw off a computation by several orders of magnitude. 4.2.2
Conflating background information and evidence
With this in mind lets turn to Dr. Carriers argument. Firstly, what is it Dr. Carrier adds to the background information? The timing of these subsequent Christians he mentions as being part of our background evidence as well as their extent within christianity is important. If “subsequent Christians” means some Christians around year 1300CE believed Jesus was historical this is true, however this would prove a version of mE (the 1300CE version) which would have no relationship to the actual evidence which is from the first two centuries.
25
Thus, the statement must imply that Christians in the early phase of christianity believed Jesus was historical. So how is this included in our background information? Dr. Carrier does not say, but it must relate to early sources such as Paul or the Gospels. The point is that Paul and the Gospels is elsewhere treated as evidence as are other early sources. So what Dr. Carrier says is that some (unspecified) part of the evidence, e0 , is actually part of our background knowledge and given this piece of evidence mE is certain. Lets state this formally. We assume that our background knowledge is composed of two parts: b = b0 .e0 where e0 : subsequent Christians believed Jesus was historical and then it is true that P (mE |¬hB .b0 .e0 ) = 1 However now our prior for hB is actually: P (¬hB |b) = P (¬hB |b0 .e0 ) So when we compute our prior probability that Jesus was not historical, we must do that while assuming (and accounting for) early Christians believing Jesus was historical. That is, e0 must explicitly enter in the argument and be well-accounted for by whatever computation we carry out. Comparing to the trial example, this is exactly similarly to the way adding a0 to the background information must be accounted for. Another way of writing this is by the ratio of the probabilities which becomes: P (e0 |hB .b0 ) P (hB |b0 ) P (hB |b) = × 0 P (¬hB |b) P (e0 |¬hB .b ) P (¬hB |b0 ) It seems plainly obvious to me at least that an early belief Jesus was historical in the Christian community e0 is easier explained if we assume Jesus was historical than if we assume he was not. For instance, it is much easier to account for an early Mormon belief Joseph Smith was historical under the assumption he indeed was. In this case P (e0 |hB .b0 ) > P (e0 |¬hB .b0 ) and so P (hB |b) P (hB |b0 ) > P (¬hB |b) P (¬hB |b0 ) So it seems reasonable to assume that when Dr. Carrier adds this piece of evidence to the background knowledge he favors mythicism. How much? Is it 5% or an order of magnitude? I don’t think there is any way to tell in general, and before we can even begin to make guesses we must know exactly what is being added to the background information; something which Dr. Carrier is very vague about. I will return to the effects of conflating various pieces of background evidence with the prior when I discuss how Dr. Carrier numerically estimates the prior.
26
Conclusion Dr. Carrier adds various assumptions mA , . . . , mE to his initial hypothesis. These additional assumptions are made in knowledge of how the evidence actually is and they serve as to make the evidence far more probable on mythicism. The effect of this is to create a bias in favor of mythicism in that the evidence is then easier to explained. How much? As all probabilities are guessed I don’t think there is any way to tell, however as we saw earlier a bias of just a few percent is enough to throw the computation completely off. The way these assumptions are justified by Dr. Carrier is by conflating various pieces of information about early christianity, presumably parts of the evidence, with our background knowledge. Before we can even begin to consider this we must be extremely clear about what constitute background evidence, evidence and hypothesis. This is not clear in On the Historicity of Jesus, rather there is a 176 pages of “background information” all of which must be accounted for when computing the prior probability and, as in the case of Bob, each piece has the possibility of invalidating the computation. To summarize: • The notation in On the Historicity of Jesus indicate two binary exhaustive hypothesis are being tested h and ¬h, however in reality what is being tested are two theories which are not mutually exclusive, each which are a mix of an (never explicitly stated) basic historical hypothesis hB and other additional elements mA , . . . , mB and h0A , h0B , h0C • Adding elements to our basic theory can (and as I argued do) bias the probability of the evidence by a large amount; since everything is guessed we have no way to track this error, but a few systematic percent is (as we have seen) enough to throw off the entire computation • The addition of additional elements to our basic theory is justified by essentially adding parts of the evidence to the background knowledge; what is added is never stated, nor is it clear how we should account for this when estimating the prior probability. If not accounted for accurately, this will arguably bias us towards mythicism • Thus, when we try to compute the prior probability of historicity or mythicism, these are really posterior probabilities based on the (never clearly specified) parts of the evidence which has been conflated with the background knowledge. Thus, the earlier example with the weight of the apple is apt: We are “proving” one posterior probability by “guessing” another posterior probability and increasing the error in our guess by combining it with other guessed probabilities • If we consider the trial example with Bob, is it the first presentation (i.e. just guilty or not) or the last presentation (with the compound hypothesis and the conflated evidence and background information) that corresponds to a disinterested objective evaluation of the evidence towards Bobs guilt? The presentation in On the Historicity of Jesus embodies the same moves as the later presentation. 27
5
Prior bamboozlement
As shown in the last section, Dr. Carrier does not test two exhaustive hypothesis for historicity, but rather two compound theories. The only way this can be justified is by assuming our background knowledge contains information specific about christianity and, as seen in the example with Bob, this requires us to be extremely careful when computing the prior probability. In other words, the argument for the prior is that makes or brakes On the Historicity of Jesus.
5.1
The Rank-Raglan prior of historicity
The prior P (h|b) is the only number in On the Historicity of Jesus which is established by a computation. As we saw earlier, this computation must account for both the (i) compound hypothesis and (ii) the conflation of evidence with background knowledge. Since this is the key step for the argument in On the Historicity of Jesus to work it is worth going over the computation details. First, Dr. Carrier introduces the Rank-Raglan hero type: Finally, the most ubiquitous model ’hero’ narrative, which pagans also revered and to which the Gospel Jesus also conforms, is the fable of the ’divine king’, what I call the Rank-Raglan hero-type (...) This is a hero-type found repeated across at least fifteen known mythic heroes (including Jesus) — if we count only those who clearly meet more than half of the designated parallels (...) The twenty-two features distinctive of this hero-type are: 1. The hero’s mother is a virgin. 2. His father is a king or the heir of a king. 3. The circumstances of his conception are unusual. 4. He is reputed to be the son of a god. 5. An attempt is made to kill him when he is a baby. 6. To escape which he is spirited away from those trying to kill him. 7. He is reared in a foreign country by one or more foster parents. 8. We are told nothing of his childhood. 9. On reaching manhood he returns to his future kingdom. 10. He is crowned, hailed or becomes king. 11. He reigns uneventfully (i.e., without wars or national catastrophes). 12. He prescribes laws. 13. He then loses favor with the gods or his subjects. 14. He is driven from the throne or city. 15. He meets with a mysterious death. 16. He dies atop a hill or high place. 17. His children, if any, do not succeed him. 18. His body turns up missing. 19. Yet he still has one or more holy sepulchers (in fact or fiction). 20. Before taking a throne or a wife, he battles and defeats a great 28
adversary (such as a king, giant, dragon or wild beast) 21. His parents are related to each other. 22. He marries a queen or princess related to his predecessor. (On the Historicity of Jesus p. 229) That is, Jesus is argued to be of the Rank-Raglan hero type because he matches 20 of the above criteria. Dr. Carrier then computes the probability Jesus existed as: 7 #{members of the Rank-Raglan class who existed} + 1 #{members of the Rank-Raglan class} + 2 0+1 1 = = ≈ 6% 14 + 2 16
P (h|b) =
This is essentially the the Rank-Raglan hero count. A nice aspect self-consistency checks 5.1.1
full extend of the argument: Because Jesus belongs to type, the probability he existed is 6% by a simple head of Bayesian probabilities is that it allows us to make of the assumptions we make so lets begin there.
Jesus almost certainly didn’t exist because four written accounts says he does
Suppose we only knew about Jesus through the Gospels. So we don’t have access to all the other historical information, but only assume we have the four gospels which describes Jesus birth, family, life, disciples, death, etc. and we assume everything Dr. Carrier says in On the Historicity of Jesus is true. Then Dr. Carrier treats all of the Gospels in a long chapter wherein he conclude they are literary inventions. The chapter concludes as follows: For now, my conclusion is that we can ascertain nothing in the Gospels that can usefully verity the historicity of Jesus. But neither do they prove he didn’t exist. As evidence, they simply make no difference to that equation. (On the Historicity of Jesus p. 509) That is: P (Gospels|h.b) = P (Gospels|¬h.b). If we combine this with the prior probability of h, which we just computed, we can compute the probability of historicity given the information in the Gospels to be: P (Gospels|h.b)P (h|b) = P (h|b) P (Gospels|h.b)P (h|b) + P (Gospels|¬h.b)P (¬h|b) = 6.25% (3)
P (h|Gospels.b) =
7 The
1 and 2 comes from Dr. Carriers use of the rule of succession.
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So if we are only given the information in the Gospels, that is, forget everything about Paul, the inconsistencies between Paul and acts, the ascension of Isiahs or the silence of first and second century sources, if we only had the Gospels we should conclude Jesus most likely did not exist. In fact our realistic estimate should be there is a 93.75% chance he did not exist. I am not a historian, but I simply have great difficulties accepting this conclusion. In other circumstances, suppose we had something like the Gospels but written about a 17th century guru in India who is described to have a family, a ministry and a death at the hands of the authorities. Sure, I would be willing to doubt that the guru had existed because of the supernatural elements in the text, but I would still think he plausibly had in fact lived. I would follow this logic: Either the Gospels (about the guru) are completely unreliably, in which case I do not know if the guru did exist or not, or alternatively they are slightly reliably, in which case them placing the guru on earth with disciples would indicate the guru more possibly than not had lived. At either case, this leaves me with a probability at around 50% and upwards he lived. The reader should draw his or her own conclusion, however there seems to be a clear inconsistency in asserting the Gospels “simply make no difference” and concluding that on the Gospels alone, we can know with near certainty Jesus did not exist. 5.1.2
A close reading of the Gospels
But there is an even more stunning aspect to this conclusion. A computation similar to the above leads us to P (¬h|Gospels.b) = 93.75% using the numbers in On the Historicity of Jesus. But recall that ¬h is Dr. Carriers theory for mythicism, that is it includes that Jesus died, was buried and raised from the dead in the supernatural realm. A person who accepts Dr. Carriers argument therefore has to feel confident with the conclusion: Given only the information in the Gospels and b, there is a 93.75% chance that Jesus did not exist and that early Christians believed he died, was buried and raised from the dead in the supernatural realm. But is it Luke, Mark, Matthew or John where we can find Jesus supernatural resurrection? At this point, I think it is quite evident something has gone amiss.
5.2
What reference classes can’t do
The underlying logic in Dr. Carriers computation of the prior is as follows: Suppose we wish to compute the probability of A given B, P (A|B). We can then count the number of known things which match B, nB , and the number of things which matches both A and B, nAB , and compute #{Things which have both properties A and B} #{Things which have property B} nAB = nB
P (A|B) =
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For instance suppose I wished to estimate the probability of Lisa having a fever given she has have influenza I could do this as follows: P (fever|influenza) =
#{People who have both fever and influenza} . #{People who have influenza}
So far so good. However suppose that we want to compute a probability such as P (h|b), that is, the probability Jesus was historical given our background information. The problem is when we ask about people who match our background information b and matches h these pieces of information are so specific no other person known through history other Jesus will match the information exactly and then nhb = nb = 0. The “fix” to this problem is as follows: When we wish to compute P (A|B), we define: n ˜ B as the number of things which approximately matches or are alike B (the B reference class) and n ˜ AB as the number of things which approximately matches or are alike both A and B (the as before. AB reference class) and then compute P (A|B) ≈ n˜n˜AB B In Dr. Carriers computation the “alikeness” was obtained by replacing b, the background information, with B: “is a Rank-Raglan hero type” and the hypothesis h with A : “is historical”. (recall that h was the hypothesis that Jesus is historical and is therefore to narrow). A problem should immediately be evident, namely that we are free to choose the reference class and different choices of reference class gives different values of the prior. Dr. Carrier is aware of this ambiguity and briefly discusses a few other choices (such as “people called Jesus Christ”) but settles on the Rank-Raglan reference class. The reasons are difficult to summarize but are in the main both pragmatic and because it is thought not to matter: The Rank-Raglan class is also a larger class with more data points in it, thus it affords us better evidence to estimate frequencies from. When we combine both facts (that ’historical’ Josephan Christs tend not to be Rank-Raglan heroes; and we have a lot better evidence for Rank-Raglan heroes), we cannot warrant using the Josephan class over the Rank-Raglan class. But it really wouldn’t matter anyway. Even if we used the Josephan Christ class, the fact that Jesus is also in the Rank-Raglan class would still have to be accounted for, and that would go into the remaining evidence. (On the Historicity of Jesus p. 246) Let me not mince words because this is an important point: Dr. Carriers use of the Rank-Raglan hero class to estimate the prior probability is very poor practice. It should not be regarded as a pragmatic compromise but as a highway to troubles. Computing prior probabilities of unique events in this manner is not found in any textbook about probability theory because it can only be considered accidentally correct. The reason why this is such a poor idea is because we are throwing away relevant information. When we say that we consider a class of things which are
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alike another we are throwing away specific information. In ordinary (frequentistic) statistics people of course approximate probabilities in this way all the time, but that is because frequentistic statistics limits itself to events which come in well-defined references classes. For instance, in the influenza example with Lisa we considered large, broad classes (fever and influenza) and (importantly!) the information about Lisa was non-specific (we only knew she had fever). In the case of christianity this is not so. Dr. Carrier himself spends 176 pages to provide background information, much of it relevant to christianity, and as we saw in the previous section considered instrumental to establish a high prior probability of the compound hypothesis. 5.2.1
Adding properties
Asides the above issue, an additional aspect of Dr. Carriers application of the Rank-Raglan reference class is that asides treating the background information in a hap-hazard manner, it does not even seem to take Dr. Carriers own hypothesis of myth into account. When we for instance wish to compute P (¬h|b), then recall that ¬h contains “died, was buried and raised in the supernatural realm” and so an immediate application of the definition of a reference class, , provides us with (again, using Laplace’s rule of succession): P (A|B) = nnAB B ( ) Is a Rank-Raglan hero and is not historical and was 1 + # thought to have died, been buried and raised in the supernatural realm and ... P (¬h|b) = . 2 + #{Is a Rank-Raglan hero} However this is obviously different from what Dr. Carrier computes namely: P (¬h|b) =
1 + #{Is a Rank-Raglan hero and is not historical} . 2 + #{Is a Rank-Raglan hero}
To put this very bluntly, the above step where we exclude a property embodies the following fallacious statistical syllogism: James is a man. 30% of all men are bald. Therefore, there is a 30% chance James is bald and likes Hip-Hop. Obviously, the problem is that if we only know that “30% of all men are bald”, we should not conclude we can throw in an additional property and conclude that there is a “30% chance James is bald and likes Hip-Hop”. The same kind of error is at work here since we try to conclude that Jesus was not historical and died, was buried and raised in the supernatural realm etc. by comparing him to the frequency of heroes about whom we only know they were not historical. As a final point before considering the prior in more details. When Dr. Carrier says we can always account for information later, this assumes the probabilities are actual Bayesian probabilities not reference-class based approximations. It also assumes a specific computation which actually accounts for how this should be done which is not found in On the Historicity of Jesus. 32
5.3
Bobs lawyer computes a prior
Just to give an idea about the problems we get into, consider the case of Bob. We could consider Bobs reference class to be people who are guilty vs. those who are on trial: P (g|b) =
#{People who are accused and guilty} . #{People who are accused}
However in the example with Bob we shifted around the relevant evidence two times; if we just defaulted to this way of estimating probabilities from reference classes we would at least once have been off by a factor of about 10 000. With Dr. Carriers argument the problem is the same but just much, much worse. For instance the inclusion of evidence into the prior information must be accounted for when we compute the prior probability, else our result can be off by orders of magnitude. This is a definitive error in the argument put forth in On the Historicity of Jesus. Regardless if the conclusion is true or not, it cannot said to have been demonstrated at this point. The reader might be disappointed that the review does not boil down to a clever argument, however it is up to Dr. Carrier to establish that the computation works and the use of reference classes, in particular the exclusion of information under vague promises that it can be accounted for later, just do not cut it. Nevertheless I will try to examine the Rank-Raglan argument slightly more and provide additional examples of why it gets us into problems.
5.4
The Rank-Raglan prior examined
It is difficult to seriously examine the Rank-Raglan prior since it is methodologically flawed from the outset. I suppose the first observation we should make is that to say Jesus belongs to the Rank-Raglan hero class is to say Jesus was said to be born of a virgin, that he was thought to have been attempted murdered as a baby, etc. etc. for all the Rank-Raglan criteria. But these pieces of information are known through the Gospels (characteristically, On the Historicity of Jesus is unclear on this point). In addition, the full set of background knowledge b contains information which does not match e.g. Romolus or the other hero types. We should then separate the evidence in the gospels and the background information into two parts: that which is used to establish 20 of the 22 Rank-Raglan criteria, ERR , and the rest of the information in the Gospels and the background information Gospels0 : Gospels and b = Gospels0 and ERR So in this Gospels0 should in principle contain parts of b, however the treatment of reference classes is so flawed a reader who find this confusing can overlook this point for now. If we accept Dr. Carriers argument then given someone belongs to the Rank-Raglan reference class then the probability of that person being historical is 6%, then the probability On the Historicity of Jesus claims to 33
estimate (but keep in mind, we still have the problem that h is far too specific a hypothesis for this to work) is: P (h|ERR ) ≈ 6%. And we could then compute the probability Jesus was historical as P (h|Gospels.b) =
P (Gospels0 |ERR .h)P (ERR |h) P (Gospels |ERR .h)P (ERR |h) + P (Gospels0 |ERR .¬h)P (ERR |¬h) 0
So as in the previous section, we see a conflation of the background information with parts of the evidence, in this case seemingly parts of the Gospels; I say seemingly because nowhere is any of this really made clear. As in the previous sections, for this to be a trustworthy procedure we have to define our background information to actually corresponds to ERR and then figure out the probabilities of the remaining evidence, for instance P (Gospels0 |ERR .h) given this new background evidence and we would still not have solved the problem that this way of computing probabilities of specific events with “alike” events is not sound. 5.4.1
The response to the alternative reference class objection examined
According to Dr. Carrier, if we used another reference class we would still get to the same result: But it really wouldnt matter anyway. Even if we used the Josephan Christ class, the fact that Jesus is also in the Rank-Raglan class would still have to be accounted for, and that would go into the remaining evidence. (On the Historicity of Jesus p. 246) Okay, so let’s test this in practice. Lets assume we don’t use the Rank-Raglan prior, that is we let b0 be our background information without Rank-Raglan relevant information such that Jesus was (thought to have been) born of a virgin, taught people on a hilltop etc. But recall this information, ERR , is found within the Gospels, Gospels. We can then simply test Dr. Carriers claim that if we account of the Rank-Raglan information as part of the evidence rather than in the prior we should obtain the same result: P (h|Gospels.b0 ) =
P (Gospels|h.b0 )P (h|b0 ) . P (Gospels|h.b0 )P (h|b0 ) + P (Gospels|¬h.b0 )P (¬h|b0 )
Bur recall that according to Dr. Carrier: “we can ascertain nothing in the Gospels that can usefully verify the historicity of Jesus. But neither do they prove he didn’t exist”. This would appear to be the statement P (Gospels|h.b0 ) = P (Gospels|¬h.b0 ) however in this case: P (h|Gospels.b0 ) =
P (Gospels|h.b0 )P (h|b0 ) = P (h|b0 ). P (Gospels|h.b0 )P (h|b0 ) + P (Gospels|¬h.b0 )P (¬h|b0 ) 34
But P (h|b0 ) is the prior of historicity in the absence of the Rank-Raglan information whereas P (h|Gospels.b0 ) is the posterior of historicity given the Rank-Raglan information which is contained in Gospels. According to the Rank-Raglan argument, see eq. (3), we know that P (h|Gospels.b0 ) = 6.25%. So if we should trust Dr. Carrier that it does not matter how we treat the Rank-Raglan information, we should conclude 6% ≈ P (h|Gospels.b0 ) = P (h|b0 ) i.e. that the new prior P (h|b0 ) (however it is computed!) also takes a value of 6%. But how can we know beforehand that this unspecified prior should take such a low value? The underlying problem is that Dr. Carrier is trying to have it two ways. He wish to say the Gospels does not matter for historicity, P (Gospels|h.b) = P (Gospels|¬h.b), and at the same time he wish to say that a subset of the Gospels (those parts which are useful to place Jesus in the Rank-Raglan hero class) should matter a great deal, in fact enough to say Jesus almost certainly did not live. These two irreconcilable assumptions are perhaps not apparent to Dr. Carrier because he poorly defines his variables (Gospels and b). Can this be fixed? Well, one could re-define the various variables or assign different probabilities to for instance the Gospels to make the text consistent, however we would still not have solved the problem that estimating the probability of a specific event such as h using finite frequentism is a bad idea. So what are we to make of the Rank-Raglan hero class information? Folklorist expert Dr Alan Dundes writes, in a book which by the way is also authored by none other than Dr. Rank: The fact that a heros biography conforms to the Indo-European hero pattern does not necessarily mean that the hero never existed. It suggests rather that the folk repeatedly insist upon making their versions of the lives of heroes follow the lines of a specific series of incidents. Accordingly, if the life of Jesus conforms in any way with the standard hero pattern, this proves nothing one way or the other with respect to the historicity of Jesus. (In Quest of the Hero, Rank, Segal, and Dundes [1990, p. 190]) This seems like a perfectly sensible argument. Independent of the historicity of Jesus, everyone except perhaps very strongly believing Christians agrees the Gospels are to some extend made up. If a Gospel writer decided to make up biographical information about Jesus, independent if he was writing with knowledge of historicity or not, the pattern he would follow is most plausible the pattern most people who made up biographies followed at the time which is the Rank-Raglan hero type. Thus, independent of historicity, it is easy to explain why the Gospels presents Jesus as conforming to a Rank-Raglan hero type. In fact a formal statement of this argument can be found on page 597 of On the Historicity of Jesus: P (Gospels|h.b) = P (Gospels|¬h.b). Too bad Dr. Carrier did not consistently stick with this choice. 35
To illustrate the point of how arbitrary the use of Rank-Raglan hero type is I will in the next two sections “prove” Jesus existed: 8 5.4.2
First “proof” Jesus existed, the written account reference class
Suppose that rather than the Rank-Raglan hero class I consider Jesus as belonging to the class of People who, within 50 years of their supposed life b50 : time, are being written about as actually living people in accounts which are not novella, etc. If we assume Jesus lived in year 30 and Mark is written around year 70 Jesus would belong to this class on account of the Gospels; meanwhile, this class would exclude many mythical figures such as Zeus, Moses, etc. While it is not clear, I believe under Dr. Carriers assumptions the background information already contains b50 . Gospels and b = Gospels00 and b50 . Where Gospels00 contains the content of the Gospels. However the people in the class b50 who can be confirmed to be historical by far outweighs those who can be confirmed not to be historical. Lets suppose for the sake of argument they outnumber the historical characters four to one, that is P (h|b50 ) = 45 . We can then compute P (h|Gospels.b) P (Gospels00 |h.b50 ) P (h|b50 ) = × 00 P (¬h|Gospels.b) P (Gospels |¬h.b50 ) P (¬h|b50 ) Consider a factor such as P (Gospels00 |¬h.b50 ). We can repeat Dr. Carriers argument: “we can ascertain nothing in the Gospels that can usefully verify the historicity of Jesus. But neither do they prove he didn’t exist. As evidence, they simply make no difference to that equation.” and conclude P (Gospels00 |h.b50 ) = P (Gospels00 |¬h.b50 ). However we then arrive at the conclusion that P (h|Gospels.b) = 80%. We can then return to Dr. Carriers remark that “But it really wouldn’t matter anyway (..) the fact that Jesus is also in the Rank-Raglan class would still have to be accounted for, and that would go into the remaining evidence.”. As I stated this is true, and the evidence of the Rank-Raglan hero class is in the above contained in Gospels00 . However when dividing the evidence in this way it is much harder to account for especially when we admit a remark to the effect that the Gospels contains nothing of use in verifying the historicity of Jesus. Take the virgin birth (which is one of the Rank-Raglan criteria). Is it more plausibly that the virgin birth was invented given Jesus was “A historical person mythisiced” or that the virgin birth was invented if Jesus was a “mythical person historiziced”? In both cases, we assume that the character of Jesus 8 These
proofs are intended as parodies.
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has been subject to legendary development, so is legendary features unexpected in either case? Things brings me to another important point. We do have plausible hypothesis why Jesus is said to be born of a virgin, namely that it is due to a misreading of scripture by later Christians. So what we really ought to evaluate is how plausible that causal mechanism is assuming historicity or myth. The use of reference classes lures us into treating dissimilar cases as similar for pragmatic reasons, thereby ignoring important historical information. 5.4.3
Second “proof” Jesus existed, the Josepheus reference class
As stated earlier, one of the key problems with the use of “reference classes” is that they necessarily throw out specific information to the hypothesis we are investigating. To take the quote above by Dr Dundes, in the specific example of Jesus what the Rank-Raglan criteria means is that subsequent Gospel writers, aware of a historical Jesus or not, decided to remake the Jesus myth so as to contain Rank-Raglan elements. This is important causal information and Dr. Carriers use of reference classes simply erases it. Dr. Carrier seems to be aware (or sort-of aware) that from a common-sense perspective this makes little sense, but as it often happens he dismisses this common-sense concern based on an invalid pseudo-technical argument: Doesn’t this presuppose that Jesus began as a Rank-Raglan hero? No. Even if his story was rebuild so that he would only belong to that class later (for example, if Matthew was the first ever to do that), it makes no difference. Regardless of how anyone came to be a Rank-Raglan hero, it still almost never happened to a historical person (in fact, so far as we can actua1ly tell, it never happened to a historical person, ever). Many of the heroes in that class may well have also begun very differently and only been molded into the Rank-Raglan hero type later. Thus, being conformed to it later has no bearing on the probability of this happening. The probability of this happening to a historical person, based on all the evidence of past precedent that we have, is still practically zero. (On the Historicity of Jesus p. 244) The gist of this argument is that now that Jesus belongs to the class we have to deal with it, regardless of how he may have entered into the class because this happened rarely to historical persons in either case. Of course ignoring causal information in this way is wrong which I will try to illustrate with an extreme example. In On the Historicity of Jesus Dr. Carrier argues in that Josepheus mentioning of Jesus is most likely a later interpolation and so has no effect on our estimate if Jesus existed or not. I will invite the reader to accept this as true for the sake of argument. However it is still a fact our manuscripts of Josepheus mentions Jesus. Suppose J is all our Josepheus-related evidence including that which shows the Josepheus-passage is most likely a later interpolation. Then assume bJ is composed of just the information that our current manuscripts of 37
Josepheus mentions Jesus and J 0 is our other Josepheus-related evidence. As before we can write: J.b = J 0 .bJ Notice J 0 is assumed to contain the information which led Dr. Carrier to conclude the Josepheus passage is an interpolation. Suppose I insist on using bJ as my reference class and, as Dr. Carrier, argues this is sound since the other evidence Jr will still has to be accounted for and so any potential problems will be solved later. Then we can make a similar computation as before: P (h|bJ ) =
#{people in our current Josepheus manuscripts who are historical} #{people in our current Josepheus manuscripts}
If we suppose there are about 100 people mentioned by Josepheus asides Jesus and if we suppose only 4 of these are confirmed fictional then P (h|bm ) ≈ 24 25 ≈ 96%9 . The computation is then: P (J 0 |bJ .h) P (h|bJ ) P (h|J.b) = × . 0 P (¬h|J.b) P (J |bJ .¬h) P (¬h|bJ ) Consider the two terms of the form P (J 0 |h.bJ ). How would we intuitively evaluate these? Assuming the Josepheus passage is an interpolation, is it evident the probability of the other Josepheus-related evidence J 0 is affected by the historicity of Jesus? Suppose, as for the case of the Gospels, we throw up our hands and conclude this has no effect. Then we are left with the answer P (h|J.b) ≈ 96% So even assuming the passage in Josepheus which mentions Jesus is an interpolation and so contains no historical information, the methods Dr. Carrier used to establish a prior probability from the Rank-Raglan reference class allows us to conclude that given the Josepheus-manuscript information Jesus almost certainly lived. however this can’t be so since we assumed the evidence demonstrated the passage were not historical. We can go backwards and conclude that we ought (for instance) have started out with the assumption that: P (J 0 |h.bJ ) = 4%,
and
P (J 0 |¬h.bJ ) = 96%.
to obtain the more reasonable result P (h|J.b) = 50%, however if we did not know where we should end up, would we have guessed these probabilities? This example also illustrates why some of Dr. Carriers other justifications for using the Rank-Raglan hero class fails. For instance, suppose someone objected to the Josepheus reference class on the grounds that we just assumed it was 9 I am not sure if this number is too high or too low since I haven’t checked Josepheus for how often he mentions historical vs. fictional characters. The point I am making remains independent of the exact number and the reader is free to insert his or her own estimate.
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a second-century interpolation. This otherwise common sense objection can be overcome the same way Dr. Carrier overcame the common sense objection that a Gospel writers later saying Jesus was born of virgin should not affect our judgement of historicity since it primarily informed us about that Gospel writers mindset. The argument would go: Regardless of how anyone came to be mentioned in our Josepheus manuscripts [a Rank-Raglan hero], it still almost never happened to a mythical [historical] person (...) Thus, being interpolated [conformed to it] later has no bearing on the probability of this happening. The probability of this happening to a mythical [historical] person, based on all the evidence of past precedent that we have, is still practically zero. (On the Historicity of Jesus p. 244) Again the problem with this type of argument is that it is ignoring important causal information, exactly what was pointed out by Rank, Segal, and Dundes [1990]. In conclusion, if we assume the evidence clearly points to the Josepheus passage being a later interpolation, it obviously should not count towards or against historicity by any significant amount. However the way reference classes requires us to throw away information allows us to reach the opposite conclusion. For instance, while it is true that Jesus belongs to the group of people who are mentioned in our Josepheus manuscripts, and the chance of any random member of this group being historical is high, we ought to keep the contextual information in mind that what’s important about being mentioned by Josepheus (in relation to being historical) if if Josepheus actually wrote about you in ca. 90CE. In ordinary Bayesian arguments there is absolutely no problem to this as we would simply compute (suppose Jo : mentioned in the original manuscript): P (h|bJ ) = P (h.Jo |bJ )+P (h.¬Jo |bJ ) = P (h|Jo .bJ )P (Jo |bJ )+P (h|¬Jo .bJ )P (¬Jo |bJ ). And then approximate P (h|Jo ) with 95% which still leaving open the option p(H|bJ ) may be low if p(Jo |bJ ) is low. Thus, to properly make use of the available information we now need to make a model of how the variables Jo , bJ , J 0 and h relates to each other and then use this model. Similarly, the Rank-Raglan hero elements, as pointed out by Rank et al. [1990], tells us that the Gospel author made up details about Jesus. But do we really need Bayes’ theorem to conclude that Jesus being born of a virgin is a made up detail? The bottom line is this: When assigned a probability of 96% to historicity because Jesus belonged to the class of people mentioned by Josepheus and of these 96% are historical we ignored that we know more things about history. For instance we know what is relevant (for that class of people) is if Jesus was mentioned in the original documents. Trying to “re-insert” this information later seems extremely difficult; in fact impossible to do with the required accuracy in this example. The problem with applying a reference-class based method to history is that it requires comparison of multiple historical examples which are not alike and this implies the removal of information. The problems with the 39
Josepheus example are thus not Josepheus specific, they are only self-evident in the Josepheus case because we know post-hoc the result is wrong.
5.5
Conclusion
Dr. Carriers overall treatment of the prior is wrong. Firstly, it is symbolically wrong. If the prior is computed based on Rank-Raglan information found in the Gospels and not the background information b, the prior which is being estimated is not P (h|b) but P (h|ERR ), which affect the structure of equation Dr. Carrier uses. More importantly however, the entire use of reference classes to specific events such as the existence of Jesus is a misapplication of probability theory. The basic problem is that when one says that some historical example is equal to other historical examples by virtue of one property, it does not follow it is equivalent to the other example in all respects. For instance the Kiwi bird is equal to the group of birds by virtue of having a beak, feathers and laying eggs, however if I computed the prior probability the Kiwi bird could fly to be the probability any bird can fly (likely more than 95%), I would have missed the important feature that the Kiwi bird have no external wings. A similar but separate fallacy is at play when OHJ claims that the prior of ¬h, i.e. that Jesus is not historical, died and was buried in the supernatural realm etc. is simply the fraction of non-historical Rank-Raglan heroes over the total number of Rank-Raglan heroes. Quite obvious, if we decide to estimate the prior probability of ¬h as the fraction of heroes that conform to ¬h, we should include the criteria that we have defined as part of ¬h hereunder dying and rising in the supernatural realm. However this and the other elements of ¬h alone would exclude many of the Rank-Raglan heroes and on this count alone the prior seems hopelessly amiss. Dr. Carrier claim these difficulties can be overcome by simply including the missing evidence elsewhere. This is false since this requires the probabilities to be actual Bayesian probabilities and not reference-class based approximations. Secondly, even if true, the problem is that when evidence is “lumped” together you have to assign probabilities to compound statements like P (Gospels0 |ERR .h), P (Gospels0 |ERR .¬h) (recall Gospels0 included those parts of our background information not corresponding to the Rank-Raglan class). These statements are arguably too difficult to treat in practice and so our default tendency would be to assign them equal probability which can go arbitrarily wrong. I tried to illustrate this danger with two examples. In the first example I used the reference class b50 , people who had been written about as if they were historical persons 50 years after their death, this gave a probability of 80% towards historicity (compared to the 6.25% computed by Dr. Carrier) assuming the Gospels makes no difference. I choose this example exactly because in my (admittedly layman) understanding of history I think the fact that people 50 years after Jesus supposed death talks about him like a human is important. In both mine and Dr. Carriers example, the other persons evidence (Rank-Raglan or b50 ) is swept into a complicated compound expression where it is ignored; I do not doubt this is unsound when I am doing it, and I therefore 40
think it unsound when Dr. Carrier is doing the same thing. The second example, based on Josepheus, also illustrates this point. Even assuming Josepheus have no historical value, we can easily arrive at an example where (ignoring the difficult compound term) there is a 95% probability in favor of historicity. This result obtains exactly because we treat reference classes naively (Jesus is mentioned in our current documents) and ignore important causal information (Jesus is mentioned in the original documents). However if we accept this type of contextual information is important for Josepheus, the Rank-Raglan criteria should also be seen in this light: By whom, how and why did the various Rank-Raglan criteria make it into our sources? According to Rank, Segal, and Dundes [1990], the context of the Rank-Raglan criteria makes them unsuitable to conclude much beyond the mindset of the writer. 5.5.1
So what is the true prior?
So if not the Rank-Raglan prior, what is the true prior for mythicism? As I have argued, I don’t think it is possible to do much beyond guessing at their values, but let’s examine what that guesswork should involve. The first problem, as noted in the previous section, is that historicity and mythicism are not defined as exhaustive propositions and so their prior probabilities will not add up to 1. Suppose therefore that we focus on mythicism. First we should of course narrow down what the different elements of the prior actually mean. Then suppose we establish a prior value for bare historicity hB , then the most crucial point would be to establish the conditional probability of propositions mA , · · · , mE in order to compute: P (¬h|b) = P (mA .mB .mC .mD .mE |¬hB .b)P (¬hB |b) However what the probability of these quantities are is pure guesswork. It appears to me it would matter a great deal to formulate the relative timing and extend to which the Christian community supposedly came to be convinced that Jesus had an earthly existence since presumably both would affect our probability. One could then tentatively begin to search for historical cases which parallel Jesus, i.e. communities within which a mythical figure became rapidly and extensively historicized along with a detailed life on earth. I cannot think of any case that parallel this development. One candidate is John Frum, the most likely mythical figure who is at the center of the Cargo Cult which arose during the second world war in the pacific, however I do not think it is known that John Frum started out a mythical figure who communicated to his worshippers in visions, and it is certainly not known that John Frum underwent death and resurrection in the supernatural realm. Other candidates could be various gods who were given an earthly life, however these Gods appear to have remained largely mythological and both the timing and extend to which it was believed these figures were historical is to my knowledge quite different. I suppose one could conclude the probability of mA , . . . , mE are one in a million and one in ten and I would not know the difference.
41
• Estimating priors based on reference classes for compound hypothesis such as is done in On the Historicity of Jesus is simply not a valid procedure. • The expression for the prior and other subsequent formula used by Dr. Carrier are formally incorrect. For instance his prior depends on information in the Gospels, and the prior he approximates is the conditional probability P (h|ERR ) and not p(h|b). • The estimated prior is at best the prior of historicity of a Rank-Raglan hero. Not the prior of the two compound theories Dr. Carrier considers. • Dr. Carriers assumptions implies the most plausible probability Jesus did not exist, assuming we only have the Gospels, is 93.25%. This seems unreasonably high. • Dr. Carrier states the Gospels have no historical value and at the same time makes assumptions which amounts to the chance Jesus did not exist given the Gospels is 93.75%. These statements are contradictory. • A general feature of reference classes applied to history is division of the evidence into two pieces: That used to establish the reference class (The Rank-Raglan related information) and the rest. Dr. Carriers assumptions, insofar as I can tell, amounts to ignoring the rest of the information, however the two other examples I came up with, the written account class and the Josepheus class, it is vital to be very careful in this division. • Dr. Carrier claims the division into two pieces of evidence is unproblematic. While I will accept this from a symbolic standpoint, it does not hold when we assign probabilities from frequencies as Dr. Carrier does. Furthermore, in practice this is far from obvious. Specifically I would be very interested in seing which arguments which does not rely on post-hoc reasoning should be used to see that the probabilities in my second example using b50 is consistent with Dr. Carriers computation. • Dr. Carriers arguments for why it is okay to ignore causal information in the use of the Rank-Raglan reference class can be applied in favor of the (trivially wrong) Josepheus class • Realistically, different reference classes leads to different results (such as 80% vs. 6.25%). If one chooses a reference class which is favorable to ones view, this will bias the entire computation. The comments from the past sections apply: Errors are magnified by about a factor 5, even very slight systematic bias in the terms will ruin the entire computation.
6
Other comments
This section is a collection of a few other comments which are not part of the central argument 42
6.1
Not using Bayes’ theorem
On the Historicity of Jesus and Proving History argues a historical argument only has a chance of being sound if it is structured according to Bayes’ theorem. Seen in that light, it is perhaps surprising that On the Historicity of Jesus does not use Bayes’ theorem. What Bayes’ theorem would provide us with is: P (h|E.b) =
P (e1 .e2 .e3 . . . e25 |h.b)P (h|b) P (e1 .e2 .e3 . . . e25 |h.b)P (h|b) + P (e1 .e2 .e3 . . . e25 |¬h.b)P (¬h|b)
(compare to eq. (2)). We could try to fix this be re-writing the terms involving the evidence using the product rule 24 times to obtain: P (e1 .e2 .e3 . . . e25 |h.b) = P (e1 |h.b)P (e2 |e1 .h.b)P (e3 |e1 .e2 .h.b) . . . P (e25 |e1 .e2 . . . e24 .h.b) however plugging this expansion into the above equation obviously do not get us the expression used in On the Historicity of Jesus. To arrive at the expression used requires an approximation, for instance the 24 assumptions that: P (e2 |e1 .h.b) = P (e2 |h.b) P (e3 |e1 .e2 .h.b) = P (e3 |h.b) P (e4 |e1 .e2 .e3 .h.b) = P (e4 |h.b) .. . Assumptions of this form is well-known in Bayesian analysis and goes by the name of Na¨ıve Bayes. These are, of course, just an approximation of Bayes’ theorem which may be useful in circumstances. It is worth emphasizing what the various terms correspond to. For instance the term P (e3 |e1 .e2 .h.b) corresponds to the probability of 1 Clement given the hypothesis of historicity, our background information as well as knowledge of documentary silence and the twin traditions. That is, rather than considering each piece of evidence separately, we must see them in light of each other. To give an even more basic example, consider the information about (say me) • A1 : Tim Hendrix’s left hand is white (vs. not white) • A2 : Tim Hendrix’s right hand is white (vs. not white) Now suppose you believe that the chance of my (left) hand being white is the same of my white hand being white: P (A1 |b) = P (A2 |b) = 12 and consider the probability of both my left and right hand being white: P (A1 .A2 |b). Evidently this number must be 21 , however if we employ the exact same approximation as used in On the Historicity of Jesus we obtain P (A1 .A2 |b) = P (A1 |b)P (A2 |b) =
11 1 = . 22 4
The approximation almost certainly affect the computation in On the Historicity of Jesus somehow. For instance, two of the terms in the discussion 43
of Acts which lower the probability of the historical Jesus relates to certain omissions about details of Jesus life in Paul’s trial speech as well as the lack of information about Jesus family in the rest of Acts. However, as for the example with the hands, if we know the author does not care about details of Jesus when re-producing Pauls trial speech, would this not make it more likely he would generally not be very interested in details about Jesus family? The point being that just as for the example with the hands, information about one aspect of Acts should make some other aspect of acts more or less likely since they were written by the same author, just as information about one aspect of my body (the color of my left hand) make other aspects of my body more likely (the color of my right-hand). By how much? I have no idea. What we can conclude is the following: • On the Historicity of Jesus does not use Bayes’ theorem but an approximation; this appears not to be mentioned anywhere • As a consequence, the various probabilities we are asked to guess (P (e1 |h.b), P (e2 |h.b), . . . ) and which Dr. Carrier provide estimates of are not those which are actually required in Bayes’ theorem. These are far more difficult expressions such as P (e14 |e1 .e2 .e3 . . . e13 .b) • It seems impossible to quantify what effect the error introduced by Dr. Carrier will have on the final result. However as a rule, the error introduced by the approximation is likely to over-estimate the certainty of the conclusions.
6.2
What Paul really meant
The probabilities of the evidence on historicity and myth which Dr. Carrier estimates in On the Historicity of Jesus are all very nearly equal, however at other places On the Historicity of Jesus expresses very high confidence. For instance, regarding 1 Thessalonians 2.15-16 Paul says Jesus was crucified by “the Jews”. This is of course problematic from a mythicist perspective, however Dr. Carrier argues this is an interpolation. The argument is found in a footnote: But the probability that Paul would write vv. 15-16 on known background evidence is easily millions to one against. In the main text I identified five unlikely features, one of which is extremely unlikely (which I’d estimate can’t be any more likely than 1 in 10 000), and the others very unlikely (no more likely than 1 in 10 apiece, for total odds against of 1 in 10 000), which combined makes the ratio of consequent probabilities 1 in 100 000 000 (one in a hundred million) (On the Historicity of Jesus p. 569) Lets simply focus on the most convincing argument, it takes up more than one page but the gist is: But most damning is the fact that these suspect verses say God’s wrath has come upon the Jews ’to the uttermost’ (...) The only 44
thing a ’final judgment’ on ’the Jews’ in ’Judea’ can possibly have been is the end of Judea itself (as a province) and the end of the Jewish cult (in the destruction of the temple) (...) No other event makes any sense. And Paul was dead by then. (...) Not in any of Paul’s 20,000 or so words, and dozens of discussions of the Jews, is there anything like it. Paul blaming the Jews for the death of Jesus is simply unprecedented. (...) 1 Thessalonians 2.15-16 is therefore simply not anything Paul would write (On the Historicity of Jesus p. 568) So the argument rest upon the proposition that the phrase “to the uttermost” must refer to the later destruction of Jerusalem and that Paul would not condemn the Jews because he himself is a Jew and has not condemned them before. From these two arguments the rather specific probability of 1 to 10 000 is derived. This seems to be a great deal of confidence to extract from what may simply be a particular choice of words and a change of heart but lets leave this aside and look at another place where Paul is interpreted. In Galatians 4.4 Paul writes: If you are Christ’s, then you [like him] are the sperm of Abraham, heirs according to the promise. And I say that as long as the heir is a child, he’s no different from a slave. Even though he is lord of all, he is under guardians and stewards until [the day] the father has foreordained. And so we, too, were enslaved under the elements of the universe when we were children. But when the fullness of time came, God sent his son, made from a woman, made under the law, in order to rescue those under the law, in order that we might receive adoption as sons. (Galatians 4.4, my bolding) To which Dr. Carrier responds: It’s clear that Paul is speaking from beginning to end about being born to allegorical women, not literal ones. The theme throughout is that Christians are heirs of ’the promise’ (to Abraham), and as such have been born to the allegorical Sarah, the free woman, which is the ’Jerusalem above’, mean ing the heavenly city of God. Jesus was momentarily born to the allegorical Hagar, the slave woman, which is the Torah law (the old testament), which holds sway in the earthly Jerusalem, so that he could kill off that law with his own death, making it possible for us to be born of the free woman at last. This is what Paul means when he says Jesus was made ’under the law’ (...) It’s obvious to me that by ’born of a woman, born under the law’ Paul means no more than that Jesus was, by being incarnated, placed under the sway of the old covenant, so that he could die to it (and rise free, as shall we). So the ’woman’ here is simply the old covenant, not an actual person. (On the Historicity of Jesus p. 578)
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But Paul remains inconvenient: Then after three years I went to Jerusalem, to consult with Cephas, and I stayed with him for fifteen days, but I did not see any other of the apostles, except James the brother of the Lord (1 Galatians 1.19) I cannot fully summarize the argument why Paul does not refer to the brother of the Lord when he says the brother of the Lord here but it begins: Here I believe this is another fictive kinship title, not a reference to James literally being the brother of Christ. We’ve already seen how Paul can use the phrase ’brother of the Lord’ to mean Christian, since all Christians were brothers of the Lord, and why Paul would have needed to be more specific if he meant ’brother of the Lord’ by birth and not adoption. So here he may be simply saying the same thing, that James was a fellow brother in Christ. Indeed, Paul goes on to say that this James (unless he means a different one) was one of the three pillars of highest repute in the church, ’James and Cephas and John’ (Gal. 2.9). The Gospels imagine these three as disciples, not the family of Jesus. In fact, the Gospels uniformly report that this James and John were the brothers of each other, not of Jesus. Might Paul have only known them as such, too? (On the Historicity of Jesus p. 587) In reality there is a probability Paul is talking about the (physical) brother of Jesus and a (physical) woman. How large are these probabilities? Dr. Carrier appears to be very confident they are small, however it is difficult not to get the impression of some bias in Dr. Carriers above arguments. For instance, in the argument regarding the brother of the Lord, Dr. Carrier notes that the Gospels may talk about the same James but as a brother of John, and so Paul might too believe that too. But on the other hand he may not and in fact didn’t we just in the previous section hear that the Gospel writers are unreliable when it comes to establishing if Jesus existed or not? Now it seems like a genealogical claim in the Gospels which may be about the same James is used to lead credence to an interpretation of Paul which (to my mind!) goes against the direct reading of the text. Finally there is Romans 1.3 which says Jesus was made from the sperm of David: [T]he gospel of God, which he announced in advance through his prophets in the holy scriptures, concerns his Son, who was born from the sperm of David according to the flesh, who was appointed to be the Son of God in power according to the spirit of holiness by resurrection from the dead, in other words Jesus Christ our Lord, through whom we received grace and apostleship, into obedience of faith among all the nations, for the sake of his name, and among whom you, too, are called to be Jesus Christ’s (Romans 1.1-6) 46
Which Dr. Carrier takes as referencing a so-called “cosmic sperm bank”: (...) If this passage [2 Samuel 7.12-14a] were read like a pesher (Element 8), one could easily con clude that God was saying he extracted semen from David and held it in reserve(...) It would not be unimaginable that God could maintain a cosmic sperm bank. After all, God’s power was absolute; and all sorts of things could be stored up in heaven (...) The notion of a cosmic sperm bank is so easily read out of this scripture, and is all but required by the outcome of subsequent history, that it is not an improbable assumption. And since scripture required the messiah to be Davidic, anyone who started with the cosmic doctrine inherent in minimal mythicism would have had to imagine something of this kind. That Jesus would be made ’from the sperm of David’ is therefore all but entailed by minimal mythicism. (On the Historicity of Jesus p. 576-577) When you try to detect bias in yourself, it is often a good idea to imagine how you would reason if the evidence had come out the other way: • Suppose it had been the Gospels that had said James was the brother of the Lord and Paul had said that James was the physical brother of John; I doubt Dr. Carrier would have bothered with an argument that Paul may have had it wrong because of what the Gospel writers had to say on the matter. After all, what does the gospel writers know?. • Suppose Paul had never mentioned a brother of Jesus, would that not have been seen as another example of suspicious silence about Jesus family which Dr. Carrier points to elsewhere10 • Suppose Paul had not said that Jesus was made from a woman, but rather that Jesus was not made from a woman. Consistent with the above, Dr. Carrier should point out that little should be made of this claim which might otherwise would seemingly support mythicism 100% because Paul was plausibly talking about a spiritual woman; in fact, Paul might be saying Jesus was not made from a spiritual woman and so in fact this should lend credence to historicity(!?). • Suppose Paul had said Jesus was not made from the sperm of David according to the flesh. To be consistent, Dr. Carrier would then argue that this means he was not made from a cosmic sperm bank, so in fact 10 For
example, On the Historicity of Jesus p. 574: “The probability that none would come up, in any manner clearly locat ing them in earth history, is certainly not ’100%’, as if we expected every specific historical fact about Jesus to be completely ignored by Paul and all his congregations and opponents-indeed, as if we expected this with such certainty that it would be surprising if he mentioned even one! No, it’s quite the other way around. The probability of this must be less than 100%. Whereas this silence is essentially 100% expected on mythicism.”
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Paul should then be taken as supporting historicity as (presumably) a person not made from a cosmic sperm bank is more likely to have been made the natural way. I don’t want to draw any hard conclusions based on this chapter because it is referencing historical claims. However I am left with the following impressions: Firstly, another way to interpret these passages is of course that when Paul talk about the brother of the Lord he is talking about the brother of Jesus, and when Paul is talking about a woman giving birth to Jesus he is talking about a woman giving physical birth to Jesus, and when he is talking about Jesus being made according to the flesh he is talking about actual flesh. I tried to get an idea about the mainstream view of these passages by starting a thread on the Biblical criticism & history forum 11 . The general consensus appears to be that scholars are either divided over Dr. Carriers interpretations or would tend to disagree with Dr. Carrier. My point is not to discredit the conclusion of On the Historicity of Jesus based on the mainstream view, but rather that it would be reasonable to say there is some probability the passages above may refers to an earthly existence of Jesus or not. However if that is the case (and the particular view would be problematic for mythicism, such as Paul believing Jesus was made from a physical woman), these probabilities has to be taken into account when computing the probability for historicity and it would increase our uncertainty in our estimates of the various terms. For instance, suppose Dr. Carrier had started from the mainstream view when assessing his conservative probability of mythicism, i.e. assumed Paul was talking about a physical brother of Jesus. Would this alone not give a probability of historicity near 1?. Secondly, I think it is possible to detect some bias in Dr. Carriers arguments. I do not doubt that there is some amount of historical information Paul could have included which would have convinced Dr. Carrier mythicism was false, however I think the bar is being set quite high. This is just my personal impression and the reader should form his or her own opinion. Thirdly, in explaining the evidence we quite clearly see the peculiar formulation of mythicism (as opposed to bare mythicism historicity) at work. For instance in the discussion of the cosmic sperm bank: “anyone who started with the cosmic doctrine inherent in minimal mythicism would have had to imagine something of this kind”. This is exactly in parallel to the example of Bob and the defence lawyer where a theory makes the evidence very easily explained and similar to the comment made about the demonic crucifixion earlier.
7
Discussion
What are we to make of On the Historicity of Jesus? Dr. Carrier brings up many interesting historical facts and perspectives which I found both interesting and challenging. Needless to say nothing negative I have to say about other aspects of On the Historicity of Jesus affects these sections, and I hope the historical case 11 see
http://earlywritings.com/forum/viewtopic.php?f=3&t=2196
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and interpretations offered by Dr. Carrier will be seriously evaluated regardless of any formal issues in his application of Bayes’ theorem. Sometimes Dr. Carrier appears to interpret evidence quite different from mainstream academia, and it would have been interesting if more focus had been put on the majority view in contrast to his own, for instance in relationship to the various quotes from the Epistles I discussed above. It would also have been interesting with a discussed of how an acceptance of mainstream ideas on authorship and interpretation affected the historical case he proposes.
7.1
Bayes’ theorem and history
As I discussed in the introduction, Bayes’ theorem can be applied to history in two ways, a qualitative way as a structuring of an argument and a quantitative way in which probabilities are guessed and combined as in On the Historicity of Jesus. I remain sceptical if the quantitative application has any real utility. I think the main take-home messages from On the Historicity of Jesus is that this requires one to take very serious the effect that comparing two compound theories (i.e. historical scenarios) can bias the computation very easily. Any such application should also be seen in the light of the initial discussion on errors, that it can be expected that Bayes’ theorem will inflate the errors in whatever guesses are made on the various terms in Bayes’ theorem. This is not a general attack on Bayesian probabilities but simply a reflects that the modelling situation we face in history is very different than in ordinary Bayesian analysis. In ordinary Bayesian analysis we have data and a model which directly models the data from explicit assumptions. For instance, we may have a variable that directly reflects the chance someone is ill as well as medical records reflecting the disease-state of many patients. In this case we do not have to guess all the terms P (ei |h) —they are build directly into the model— and the availability of data (the patients records) ensures the model has enough information to overwrite inaccurate prior assumptions. In addition we can validate that the model is correct by making predictions on unobserved hospital records. In this case it does not matter there is a subjective component in our assessment of the priors since enough data will eventually overwrite any false prior assumptions. However when we compare to historicity we only have subjective judgements in all terms and no way to validate the model. If I had to assess such a project in other circumstances I would say it was not worth bothering.
7.2
Summarizing the counter-argument to On the Historicity of Jesus
On the Historicity of Jesus contains many imprecisions and omissions of important details which makes the argument difficult to examine in details. The only place where Dr. Carrier can be said to go formally wrong in a strict sense is in the assignments of priors, however it is important to stress that the lead-up
49
to that error is important too. To summarize the full (erroneous) argument by Bobs lawyer in the DNA case it was: • Rather than considering binary propositions (not guilty vs. guilty), Bobs lawyer consider compound propositions (not guilty+error at the laboratory vs. guilty). The compound proposition makes the evidence far more probable. • Information which would otherwise be considered evidence (that Bob was arrested by the police) is moved into the background information to argue the probability of (one aspect of) the compound proposition is very likely true (“Since Bob is not guilty and he was arrested, this must be because the police made a mistake, so the chance the DNA sample is contaminated is very high”) • These moves may be formally true, however they require us to estimate much, much more complicated probabilities however— • Bobs lawyer makes a simplistic and false frequentistic argument to compute the probability Bob is innocent as the fraction of arrested people vs. those who are found guilty. This is erroneous as it ignores information specific to the case. • Since the prior probability do not reflect the compound proposition nor that information has been moved from the evidence to the background information the argument is arbitrarily wrong Keep in mind that while the only formal error was made in the prior, the shuffling around of evidence and the use of a compound hypothesis will affect all terms in the computation. The argument in On the Historicity of Jesus is very similar: • Rather than considering binary propositions (historical hB vs. not historical ¬hB ), Dr. Carrier considers compound propositions (the different scenarios for mythicism and historicity) which makes the evidence far easier to explain on mythicism. • Information which would otherwise be considered evidence (the RankRaglan information and who knows what which according to Dr. Carrier makes the compound propositions likely) is moved into the background information to argue the compound proposition is very likely true • These moves may be formally true, however they require us to estimate much, much more complicated probabilities however— • Dr. Carrier makes a simplistic and false frequentistic argument to compute the probability of his (non-binary!) compound propositions as the number of historical figures in the Rank-Raglan class vs. the total number of elements in the Rank-Raglan class. This is erroneous as it ignores information specific to Jesus or Dr. Carriers specific hypothesis. 50
• Since the prior probability do not reflect the compound proposition nor that information has been moved from the evidence to the background information the argument is false. As also argued, the use of a compound propositions (the theory for mythicism) will likely bias the computation in favor of mythicism as it quite plainly makes many pieces of evidence far more easily explainable than any generic theory for mythicism. Thus, Dr. Carrier introduces a bias in favor of mythicism and as we saw earlier Bayes’ theorem is quite unstable to such a bias. For this reason I do not think the result, the chance Jesus existed is between 0.00008 and 0.3233, has been established.
7.3
Final comments on On the Historicity of Jesus and Proving History
I think someone who wish to apply Bayesian methods to history should make sure he understands what Baysian reasoning can accomplish and what it cannot. Dr. Carrier has in the past made a number of remarkable claims. For instance around 2001 he believed the evidence for the big bang was inconclusive and described himself as a “Big-Bang sceptic”. In 2011 he claimed to have solved one of the greatest problems in contemporary physics by discovering a theory which explaining how quantum phenomena can be explained by general relativity alone: it is theoretically possible to deductively predict all entanglement phenomena including the results of every EPR experiment, without recourse to any special theory of quantum mechanics. (from Calling All Physicists) With the publication of Proving History, Dr. Carrier claims to have unified a Bayesian and frequentistic view of probabilities and all historical epistomology should be done using Bayes’ theorem. With On the Historicity of Jesus the existence of Jesus is computed to have a probability of 6.75%. I will leave aside the question Jesus existed, however there is a tendency that Dr. Carrier proposes or defends radical ideas outside his area of expertise. These ideas are formulated without using the common language in the domain they fall under, for instance his sceptisism of the Big-bang appeared not to make references to the cosmological standard model, the unification of quantum mechanics and special relativity does not contain any formulas or the issues which makes the problem hard and the unification of frequentism and Bayesianism consists of a loose discussion which misunderstands both what these ideas are and how they differ (I discuss these problems extensively in my review of Proving History). I am not sure where Dr. Carrier stands on the quantum mechanics proposal today, however to his credit he has realized the evidence demonstrates that the Big-Bang did indeed happen. A lesson I would suggest for Dr. Carrier is to very carefully ensure he understands a field before proposing a solution, especially if the solution appears to be 51
very simple and not requiring any particular knowledge of the problem. I think nearly any student of physics at some point intuitively realized special relativity must be wrong because obviously if two observers simultaneously can see that time has slowed down for the other observer this is a contradiction, however all good students proceed to realize that this result is entirely consistent when analysed correctly. Simple solutions are unlikely to have been missed by experts for decades. This goes doubly when the field contains mathematical material and has itself been subject to expert disagreement and failed proposals, in which case I think one as a minimum should understand the relevant science and mathematics. Dr. Carrier himself describes his frustration when engaging with physicists on the Big-Bang theory with these words: I encountered as a result a sea of snobbery and condescension from physicists, (...) I encountered bias and closed-mindedness (...) This kind of arrogance was appalling., (...) all I was ever given was a paltry handful of sometimes dubious facts that did not entail the conclusion drawn from them, (...) just as the Christian is not authorized to expect me to believe in the Resurrection without the evidence afforded to Thomas, so the cosmologist is not authorized to expect me to believe a theory that he cannot demonstrate to me as true, (...) the rude madness I received from the physics community (“I Was a Big Bang Skeptic” 12 ) Today Dr. Carrier is both recieving critisism and giving crititism on his blog and in other publications. For instance in my review of Proving History, I pointed out several difficulties in the presentation which I do not consider to have been refuted or even seriously discussed. My review is summarized on Dr. Carriers blog with the sentence: Hendrix, Tim (conclusion: only complains about things the book didnt say) 13 . I don’t pretend to be objective, however the things I discussed were specific and central to Dr. Carriers overall thesis. To take a single point which can be summarized briefly I pointed out that Dr. Carriers proposal for what a probability is (which is the central element of his unification of Bayesianism and frequentism) cannot represent a probability such as √12 . To this he replied:14 Nor will I bother with his silly attempt to insist we need to account for infinities and irrational fractions in probability theory. Nope. A fortiori reasoning does away with any such need. (Dr. Carriers blog) This is quite frustrating. Most of the points I have brought up in my review of Proving History are also discussed more briefly by Ian (I do not know his last name) from the blog “Irreducible Complexity”. Ian has a PhD in a relevant 13 http://freethoughtblogs.com/carrier/archives/5730 14 http://freethoughtblogs.com/carrier/archives/8192
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field to Baysian learning and points out the same, basic epistemological problems that I have pointed out, however his review is summarized as “conclusion: pedantic; retracted all substantive criticisms”, a characterization which is very difficult to recognize. Elsewhere, Luke Barnes, a PhD in astronomy who has both taught and published on the Bayesian approach to probabilities, discusses Dr. Carriers approach to probabilities on his review of Dr. Carriers 2013 article on the fine-tuning of the universe15 . A reader should keep in mind this article is on fine tuning, however Dr. Barnes points out many of exactly the same epistemic issues regarding probabilities that I and Ian do; My own thoughts on the fine-tuning argument can be found online 16 . Dr. Carrier describes Luke Barnes posts as “nonsense” and Luke Barnes as a “kook” and possibly “crazy”. Other critics of Dr. Carrier does not fare better, for instance Stephanie Fisher’s comments on Proving History are summarized as (conclusion: didnt read the book, lies about it; doesnt understand math; probably insane), Louise Antony’s too “doesn’t understand math” and Maurice Casey is also diagnosed as possibly insane. Having a PhD, a critical opinion of Dr. Carriers work and a mental health issue appears to go hand-in-hand. I would suggest that Dr. Carrier considers what would serve as a valid criticism for his work. As I can tell we are now three people with a PhD in a relevant field who have written on Dr. Carriers various works which uses probabilities and all have come to the conclusion that there are serious and specific deficiencies in it. When Dr. Carrier responds or addresses a criticism of a formal point, for instance the use of a particular formula, he often does so by a lengthy arguments which might be about the objection, but still fails to explain how whatever procedure Dr. Carrier advocates actually follows from Bayesian probability theory. This strategy is also evident in On the Historicity of Jesus. Take for instance the discussion of the Rank-Raglan inspired prior and Dr. Carriers discussion of why the Rank-Raglan prior is appropriate even if it ignores information. Dr. Carrier offers many justifications written as text, however none of these justifications would survive being translated into formulas. For instance, when Dr. Carrier says the use of the Rank-Raglan reference class is irrelevant because the information would have to be accounted for elsewhere, a formula which actually showed what Dr. Carrier had in mind would quickly reveal that this accounting-for-elsewhere does not take place within On the Historicity of Jesus and brings about additional difficulties. This is a general feature of Dr. Carriers writings, for instance he has yet to give a clearly-stated non-circular definition of probabilities as used in Proving History 17 or provide a response to my criticism of the his fine-tuning argument 18 . It is tempting to say that Bayes’ theorem appears not to play a very prominent role in Dr. Carriers writings. Sure he writes that he is providing a Bayesian argument and at some point applies Bayes’ theorem, however when it comes to 15 https://letterstonature.wordpress.com/2013/12/15/what-chance-looks-like-a-fine-tuned-
critique-of-richard-carrier-part-1/ 16 https://www.scribd.com/doc/296697791/Richard-Carrier-s-rough-fine-tuning-argument 17 https://www.scribd.com/doc/271358647/Richard-Carrier-Proving-History-Review 18 https://www.scribd.com/doc/296697791/Richard-Carrier-s-rough-fine-tuning-argument
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justifying why the particular application is appropriate, or respond to supposed technical inaccuracies, Dr. Carrier resorts to informally stated written arguments and justifications which draw on a huge variety of thought-experiments and poorly applied terminology when what a convincing response would come down to –if one indeed wished to apply Bayesian probabilities– would be what exact formula was used. I think this use of Bayes’ theorem is highly questionable as rather than making an argument more clear it allows to hide questionable assumptions behind terminology. For instance I have a strong feeling that Dr. Carrier, in 2008, would not have considered a later Gospel writers statement that Jesus was born of a virgin to have an impact on the historicity of Jesus since I believe he would have reasoned that the Gospels were written by people quite far removed from the historical origins of Christianity. However today this observation (along with the Rank-Raglan criteria) becomes important in establishing a low prior probability of historicity. My guess is what happened is that Dr. Carrier, based on a misunderstanding of what a reference class is and does, realized that if one used the Rank-Raglan hero reference class this seemingly fairly irrelevant piece of information could be used to assign a prior of historicity of just about 6.25%. Dr. Carrier realizes there are objections with this line of thinking, however rather than analysing these objections from a Bayesian perspective and thereby realize they are indeed to be taken serious, he dismissed them by what appears to me as post-hoc justifications based on an intuition that the 6.25% must mean something important and Bayes’ theorem must give consistent results, so starting out with this prior assignment can’t be a big deal. The disadvantage of this way of using Bayes theorem is that rather than making a Bayesian argument the engine that drives the train, it has become the caboose that is being dragged along for the ride. Having now reviewed three different books and book chapters by Dr. Carrier wherein he applies Bayes’ theorem I believe most of the difficulties comes down to epistemic issues on what a probability is and how they relate to fractions (i.e. reference classes). As mentioned, Dr. Carrier believes that all probabilities are frequencies and on this belief the use of the Rank-Raglan reference class may not seem so far fetched. This view is false according to any standard textbook view of Bayesian probabilities, to quote Luke Barnes: 19 I have 13 probability textbooks/lecture notes open in front of me: Bain and Engelhardt; Jaynes (PDF); Wall and Jenkins; MacKay (PDF); Grinstead and Snell; Ash; Bertsekas and Tsitsiklis; Rosenthal; Bayer; Dembo; Sokol and Rnn-Nielsen; Venkatesh; Durrett; Tao. I recently stopped by Sydney Universitys Library to pick up a book on nuclear reactions, and took the time to open another 15 textbooks. Ive even checked some of the philosophy of probability literature, such as Antony Eagles collection of readings (highly recommended), Arnborg and Sjodin, Caticha, Colyvan, Hajek (who has a number of great papers on probability), and Maudlin. (...) 19 https://letterstonature.wordpress.com/2016/02/05/final-word-on-richard-carrier/
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In precisely none of these textbooks and articles will you find anything like Carriers account. When presenting the foundations of probability theory in general and Bayes Theorem in particular, no one presents anything like Carriers version of probability theory. Do it yourself, if you have the time and resources. Get a textbook (some of the links above are to online PDFs), find the sections on the foundations of probability and Bayes Theorem, and compare to the quotes from Carrier above. In this company, Carriers version of probability theory is a total loner. Well see why. (Luke Barnes, “Letters to Nature”) The problem is that the intuition behind Dr. Carriers view, that all probabilities must somehow be frequencies, seems to be why he is so certain it is valid to replace probabilities with frequencies such as for the Rank-Raglan prior. Dr. Carrier is therefore simply not assuming the same foundations as textbooks in probability theory, all the while he will insist that textbook results (such as consistency results), also holds for his account. This is a gigantic bait-andswitch argument, and any attempt to discuss the specific issues in Dr. Carriers writings by Luke Barnes, Ian or I have so far digressed into a discussion of Bayesian epistemology which I do not think many lay-readers can take much away from.
Appendices A
Bayes’ theorem
I have written shortly about Bayes’ theorem in my review of Proving History and will only provide a condensed account here. What does it mean to be Bayesian? Briefly stated, Bayesianism is the idea uncertainty should be quantified using probabilities. For instance if I consider the proposition: “Bob has influenza”, my belief that statement is true is a probability. Recall a probability is a number between 0 and 1 such that 1 (or 100%) reflects certainty the proposition is true. The truth of various propositions affect each other, for instance if someone told me that Bob has a fever, this would increase my confidence that Bob has influenza. Under Bayesianism this relationship is captured by saying “X given Y”. For instance I could talk about the probability of the statement: Bob has influenza given Bob has a fever. Lets begin to translate this into math. To do so we define the propositions: A : Bob has influenza B : Bob has a fever then we will write the probability of the previous statement as: P (A|B) 55
That is, the vertical bar is read as “given” and the p as “the probability of”. The above would then be read as: P (A|B) ↔ The probability of “Bob has influenza” given “Bob has a fever” and if for instance P (A|B) = 0.9 would correspond to being 90% certain that Bob had influenza given he had a fever. We need two more ingredients. If we can consider the probability Bob has a feaver, we can also consider the probability Bob does not have a fever, and if we can consider the probability Bob has a fever we can also consider the probability Bob has a fever AND a running nose. Thus, suppose we introduce C : Bob has a running nose then and and not is written as: ¬A ↔ ”not A” ↔ it is not true that Bob has influenza ¬A.B ↔ ”A and B” ↔ Bob has influenza and Bob has a running nose With this in place we can begin to formulate the basic rules of probability theory, of which there are only two: (sum rule): (product rule):
P (A|B) + P (¬A|B) = 1 P (A.B|C) = P (A|B.C)P (B|C)
The first rule is simply saying that if we are (say) 30% certain that A is true given B then we are 70% certain A is not true given B. The second rule is more interesting and is stating that the probability A and B are both true given C is the probability B is true given C times the probability A is true given B and C are both true. With these two in place we can prove a number of important corrollaries for instance: P (A|C) = P (A.B|C) + P (A.¬B|C) why? because P (A.B|C) + P (A.¬B|C) = P (B|A.C)P (A|C) + P (¬B|A.C)P (A|C) = (P (B|A.C) + P (¬B|A.C))P (A|C) = P (A|C). Most importantly we can derive Bayes’ theorem. To make the connection to the later use more apparent I will introduce three new propositions: E : Set of available evidence h : A hypothesis we wish to examine is true or not b : Our relevant background knowledge
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For instance: E could be that Bob has a fever, h that Bob has influenza and b relevant knowledge about medicine. Then Bayes’ theorem is written as P (h|E.b) =
P (E|h.b)P (h|b) P (E|h.b)P (h.b) + P (E|¬h.b)P (¬h|b)
That is, to figure out how likely the hypothesis h is on the evidence E (the lefthand side), we can solve this problem by figuring out how likely the hypothesis is in-and-by itself (denoted P (h|b) or the prior ) and then combine this term with how likely the evidence is given the hypothesis is true, P (E|h.b) and how likely the evidence is given the hypothesis is not true, P (E|¬h.b). Lets consider an example. Suppose an average person (such as Bob) has influenza for a week every fourth year, that is the chance Bob has influenza at any given time is: P (h|b) ≈
7 Days bob has influenza in 4 years = ≈ 0.005. Days in 4 years 4 × 365
Suppose then that if bob has influenza, he will be 95% certain to have a fever, on the other hand if Bob does not have influenza we can expect him to have a fever from unrelated causes (such as the common cold) one week in 2 years. That is, P (E|h.b) ≈ 0.95 7 P (E|¬h.b) ≈ ≈ 0.01 2 × 365
We can then combine these numbers to obtain P (h|E.b) ≈ 0.323. and conclude that even if Bob has a fever, he is fairly unlikely to have influenza.
References O. Rank, R.A. Segal, and A. Dundes. In Quest of the Hero. Number pt. 2 in Mythos: The Princeton/Bollingen series in world mythology. Princeton University Press, 1990. ISBN 9780691020624. URL https://books.google. dk/books?id=bDfiFlTbWGYC. A. Tucker. Our Knowledge of the Past: A Philosophy of Historiography. Cambridge University Press, 2004. ISBN 9781139452250. URL https: //books.google.dk/books?id=siS5DK1HdwsC.
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