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What Bayesian Reasoning Can and Can’t Do for Biblical Research

27. March 2019 | Christoph Heilig | 3 Kommentare |

1. Introduction to Given’s Review and Bayes’s Theorem

Mark D. Given has recently reviewed my book Hidden Criticism? The Methodology and Plausibility of the Search for a Counter-Imperial Subtext in Paul for RBL. In this monograph, which was published as part of the WUNT II series by Mohr Siebeck in 2015 and in 2nd edition by Fortress in 2017, deals with the question of whether we can discern anti-imperial echoes in the letters of Paul.  Obviously, I like the conclusion of Given’s review very much:

“… chapters 3–6 brim with more critical insights than I could possibly mention. The author is to be highly praised for his mastery of relevant research displayed throughout this book and the incisive and judicious commentary he provides on it. Hidden Criticism is an important contribution to scholarship on the subject of Paul and empire and a must read for anyone seriously interested in the topic.”

Given also identifies one area, where he is not that happy with my book and I think his criticism is worth being quoted in detail here. Since James McGrath has also posted about this on his blog (with several insightful comments under the original post), I’d like to take the opportunity here of deepening the conversation on this subject by on the one hand reflecting critically on some of the things I wrote in Hidden Criticismand by also, on the other hand, re-emphasising some aspects that have been important all along to me but which I probably did not formulate clearly enough in the past.

Here’s how Given introduces his complaint:

“I only have one major criticism of the book: the use of Bayes’s theorem. …  Whether or not the theory is necessary, Heilig does not explain it well. I found myself consulting additional resources that did explain it well, and only afterward could I better evaluate what Heilig is trying to do with it.”

First of all, I am very grateful to Given that he actually went the extra mile and did additional research, something that certainly not every reviewer would have done. Accordingly, this blogpost is meant as an attempt to do justice to his effort and is not to be understood as the unsatisfied reaction by the author. Moreover, I think Given is entirely right in his criticism. I tried to keep the introduction to Bayes’s theorem as short as possible in order to avoid the impression that it might be a more central aspect than it actually was for my work – with the result that the introduction to the concept is probably way too dense. If you want to know what Bayes’s theorem is and how it might affect the way we construct arguments, I would strongly encourage you to simply watch this 10-minute-video. If you have never heard of Bayes, trust me, it is an excellent investment of your time!

2. Bayesian Reasoning Can Help Evaluate “Criteria” in Biblical Scholarship

Assuming that you’ve watched the video (or are already familiar with Bayes’s theorem anyway), I will now continue by considering Given’s conclusion about the potential benefits and limitations of Bayesian reasoning for biblical studies:

“To be sure, Heilig is explicitly clear that he is not claiming Bayes’s theorem is a methodological key that can open the door to assured results regarding the subtext hypothesis. However, implicitly he often argues as if it can, or at least that it can rule out some proposals … “

Given here touches on a very important point, namely the actual relevance of Bayes’s theorem for my book Hidden Criticism? In retrospect, I think that I might not have been clear enough on the question of why I even refer to the concept in chapter 2, which deals with the (in my view) dominant approach established by Neil Elliott and N. T. Wright of identifying a counter-imperial subtext in Paul by means of Richard B. Hays’s echo-criteria. The sole purpose of sketching the Bayesian principles was to evaluate this set of criteria. (I think that in my earlier essay-length summary of my argument this role might have been more obvious. You can access it here.)

Biblical studies is obsessed with criteria: we use them in textual criticism, life-of-Jesus-research, and intertextuality discourses, to name just a few influential areas. Criteria are meant to make the scholar’s life easier. In my experience, however, they often complicate discussions unnecessarily – sometimes even becoming the object of scholarly debate to an astonishing extent. Every year, dozens of dissertations are written that all compare different sets of criteria which have been suggested by more senior scholars to solve a specific problem, then selecting one of the sets or modifying it, and then applying it to some texts. Biographically, it made a big impression on me when during iSBL 2013 in St Andrews a doctoral student’s presentation on intertextuality basically consisted of a listing of different sets of criteria that had been suggested. When asked in the end, which one he would be choosing for his own textual analysis, he basically threw his hands up in the air, saying: “Well, if only there were a meta-criterion for assessing the validity of criteria…!”

Bayes’s theorem rather obviously offers just such a grid – and that is why it had become important for my research on counter-imperial echoes in Paul’s letters. I wanted to know: “In order to answer the question of whether there is such a subtext in Paul’s letters, can I simply – with Elliott and Wright but also Barclay – apply Hays’s criteria to these texts?”

As it turns out, considered against the background of Bayes’s theorem, Hays’s set of criteria is deeply problematic. Don’t get me wrong:  It raises some really important questions. But some of these questions overlap. So we can’t just count answers. Moreover, half of the evidential weight that should influence the scale of our decision making with regard to whether the hypothesis of an echo is more probable than the alternative is actually contributed by one of the questions! That’s why I conclude:

“In light of all of this, it does not seem advisable to use Hays’s criteria as a methodologically sound way to identify echoes. To be sure, it is possible to come to well-founded conclusions on their basis … but in these cases it is not the set of criteria itself which guarantees the success, but their wise use, which attributes the correct significance to each of them.”

Hidden Criticism, pp. 42-43

(You can see read a shorter version of my assessment of the criteria here fore free.)

One is certainly free to judge this to be a rather modest insight. However, in light of the many “applications” of Hays’s criteria it still seems quite significant to me and I am glad to see that Joel White has recently also made an effort to do justice to it in the realm of identifying scriptural allusions (see his chapter in this volume).

So, to come to an interim conclusion, one of the two ways in that Bayes’s theorem can be important for biblical studies and in that it also plays a role in my argument in Hidden Criticism is the following:

Awareness of Bayes’s theorem can prevent us from using unsuitable sets of criteria when dealing with texts or at least tell us how the different criteria are to be assessed in relation to each other.

You might not be in need of such a framework because you are an excellent thinker anyway. Personally, it helped me immensely to have a tool at hand that helps me connect the dots between the individual criteria that are brought to a text by colleagues and myself. And when I think about the confusion of students, when they have to deal with “conflicting” criteria for establishing the relationship among textual variants and when I remember the confusion and sometimes even desperation of junior researchers in trying to navigate through the literature of those who came before them, I am tempted to believe that I am not alone in that situation.

3. Bayesian Reasoning Can Help to Prevent Argumentative Fallacies

To be sure, for the rest of Hidden Criticism the theorem isn’t that important. In fact, its only significance for the remainder of the book is that it offers a certain context for understanding what chapters 3-5 are doing, namely that they are scrutinizing the “prior-probability” (or, as I called it in order to sound less mathematic: “background plausibility”) of the counter-imperial echo-hypothesis. By contrast, chapter 6 is only offering some guidance for how to evaluate likelihoods (or: “explanatory potentials”). It was important to me back then to emphasise that I was not answering the question of “how probable is the hypothesis that Paul criticised the Roman empire in coded form?” From a Bayesian perspective it can’t be any different, of course, because an assessment of the posterior-probability would presuppose an assessment of likelihoods, which, in turn, would necessitate the analysis of specific texts in the framework of the discussed hypothesis and its alternatives. I didn’t see how I could do such an analysis as part of the book, which is why I wrote a second monograph that deals with a single text (2 Cor 2:14) to fill this gap. So I do think that Bayes’s theorem is important for Hidden Criticism as a whole in that it offers a context for understanding what the book aims (and does not aim) to achieve. Unfortunately, I had been convinced to put the word “plausibility” in the subtitle of the book, which I regret. Also, the description I provided the publisher with is indeed a bit misleading (“On the basis of insights from the philosophy of science, Christoph Heilig suggests several analytical steps for examining this paradigm.”)

To come back to the more general question behind this blog post, let me summarise this aspect of the value of Bayesian reasoning for biblical studies (and in a limited extent also for Hidden Criticism) as follows:

If we keep an eye on Bayes’s theorem, it can help us to gain a realistic perception of what we are actually contributing to a research question: Are we dealing with its background plausibility? Are we assessing its explanatory potential? Are we doing both and are we doing it also for competing hypotheses so that we can actually make statements about which hypothesis is most probably true?

Given also seems to recognise the value of this second aspect for he ends his criticism by saying:

“I [would not] dissuade historians from reflecting on Bayesian reasoning in a loosely analogical way while doing their work. It can and should make us more circumspect in our use of ‘intuitions’ (34).”

The most basic disagreement (perhaps the only real disagreement) between Given and me might be the value of this contribution of Bayesian reasoning. Part of the reason for why I wrote “Paul’s Triumph” was to show that the vast majority of the different proposals for Paul’s use of θριαμβεύειν in 2 Cor 2:14 did not only miss some evidence but systematically failed to incorporate huge areas of evidence. The authors of these articles and monographs usually picked either prior-probability or likelihood as their point of departure – without ever coming full-circle. There is of course nothing to be said against such contributions to scholarship – as long as they are not associated with claims about an overall-plausibility of the thesis under discussion (which then by definition renders the contribution incomplete).

Almost every journal issue has an article on a new suggested “background” for a biblical passage. (See, for example, here on “neglected points of background.”) Mostly, the argument runs like this:

“There is some archaeological or literary evidence from other sources that indicate that the author might have been in contact with a certain cultural phenomenon. Now that we know that the author was aware of that ritual or concept, it of course becomes much more plausible to assume that he also talked about it. And that’s why we should assume that an until now mysterious text actually is to be understood against that background.”

To me it is mind-blowing to observe how often such articles do not even mention the question of whether the actual wording of the text is indeed what we would expect if this background was indeed the one on the author’s mind. Without answer the following question that encapsulates the aspect of likelihood/explanatory potential no statement about whether or not the new proposal actually offers a better explanation for the text than previous alternatives makes any sense: “would we expect the specific wording if we presupposed a proposition with counter-imperial intent?” (Hidden Criticism, p. 140). Given has some very insightful comments on precisely this issue:

“I have used a similar test with students over the years that I call the rhetorical criterion. When a student proposes an interpretation of a contested passage, I ask if these are the words we would have expected to be used to convey that meaning. Asking this question often heads off eisegesis because the student immediately sees that if the author meant what the student proposed, the wording would likely be different. Heilig uses this sort of logic to great effect while reflecting on various proposed anti-imperial passages. Whether one agrees with his specific conclusions or not, the way he reasons about these passages is worthy of emulation.”

If you think this problem is only prevalent among students, I’d refer you again to my analysis in Paul’s Triumph. I have to insist: it is not.

And for that reason, Bayes’s theorem is indeed important for biblical studies. It is of course possible to take into account the evidence relevant for prior-probability and likelihood without knowing these categories. Indeed, many good historians do so all the time (as I also clearly say in Hidden Criticism, p. 27: “Every good historical enquiry will always pay attention to both factors.”). The problem is that I’ve come to the conclusion that more often than not we (and I certainly include myself here) as biblical scholars are not actually following this example well enough.

Note also that Bayes’s theorem tells us two things about Given’s “rhetorical criterion” that one might easily overlook (i.e. I assume Given is aware of these aspects of his criterion, but I don’t think it’s so far-fetched to imagine that someone might miss them):

First, it’s possible indeed that the rhetorical criterion might “favour” (the technical term for this constellation) a specific meaning but that a different interpretation is still more probable. The reason for this is that people sometimes indeed do what is unexpected. For example, let’s take the hypothesis that in the very last paragraph of Hidden Criticism I intended to encourage research on the question of whether Paul criticised the Roman Empire in the subtext of his letters. Would you have expected me to have written “we should…  avoid this complex of questions (Hidden Criticism, p. 160)? Certainly not. But that’s exactly what I submitted to the publisher. Still, if you had read the book up to this point, your assessment of the semantics/pragmatics of this sentence wouldn’t be difficult at all, because you would already have a very clear idea about the background plausibilities of different interpretations of this sentence. (For more on this, see here.)

In other words: Given’s “rhetorical criterion” is a really helpful pedagogical tool but it offers a guide to plausible interpretations only in conjunctions with considering the aspect of background plausibility, i.e. the aspect that the aforementioned “background-studies” focus on exclusively (and unjustifiably so). If explanatory potential/likelihood is considered in isolation, there is a permanent danger of coming up with “false positives.”

You can find this kind of fallacy often associated with theses on matters of historical reconstruction that have defied an easy solution for a long time. For example, in the literature on the synoptic problem (or on problems of source criticism) you will find ever more complex solutions that aim at integrating the multitude of textual phenomena. Often, these proposals start with a rather simple core hypothesis that is over time supplemented with very many auxiliary hypotheses which need to be postulated to save the research program from the complexity of the empirical data. In the end of such a process you will necessarily have a hypothesis that will be capable of explaining each and every tiny detail of the textual tradition. However, the assertion “My theory explains all the evidence perfectly!” in itself is of little use, if this enormous explanatory potential is bought at the cost of an acceptable background plausibility.

Second, there is yet another danger for “false positives” associated with the rhetorical criterion. We’ve already discussed the possibility that the parameter of background plausibility is neglected. Another common mistake is to emphasise the good explanatory potential of a hypothesis but to overlook that there are alternative explanations, which also perform quite well with regard to the likelihood-aspect.

For example, I sometimes think that political pundits on TV also would profit a lot from some familiarity with Bayesian reasoning. Just in the last couple of days, I’ve heard so many comedians and commentators wonder why many people in the Trump orbit lied about contacts to the Russians if there was no collusion (and apparently there wasn’t). For two years, these people seem to have concentrated only on the explanatory potential of the collusion hypothesis: if the Trump team had colluded with the Russians, it is indeed quite probable that they would have lied about contacts with Russian officials (because people often attempt to cover-up criminal activities when confronted with them). However, apparently, it never crossed the mind of these individuals that (leaving aside prior-probabilities for the moment entirely) there might also be other scenarios in which lying about such contacts might be quite predictable (e.g. taking into account the human tendency to lie, private business dealings, and – last but not least – avoiding the appearance of collusion).

Third, the rhetorical criterion – the focus on likelihood/explanatory potential – can also lead to “false negatives” if used improperly. Again the problem might be the lack of comparison – which in this can lead to the false assumption that the only partial fulfilment of the rhetorical criterion could imply something negative for the overall probability of the hypothesis. That’s very problematic: Sometimes we should indeed accept a meaning even though there might have been much more common ways to express this thought. So the “rhetorical criterion” only works well if we apply it not just to a single possible meaning but to all the competing semantic hypotheses. For example, the word “ninnyhammer” might not exactly be our first prediction for how a speaker might introduce the concept of ‘idiot’ into a discourse – but it seems to me that it would be an even more awkward choice for communicating a compliment.

Thus, it seems to me that Given’s own “rhetorical criterion” powerfully demonstrates the usefulness of Bayes’s theorem for biblical studies. Sometimes, it completely suffices to ask the student whether the actual text in front of us is what “we would have expected to be used to convey that meaning.” Under different circumstances, such a shift of the perspective can, however, lead to wrong results, at least if the procedure is not specified by means of further guidelines. The art of good exegesis is to know, when this criterion in its simple form (i.e. when the focus on the explanatory potential of a single hypothesis) is actually productive. Being aware of Bayes’s theorem is one way of mastering this art.

Again, let me be very clear about these: the above considerations might be very intuitive to you. If so, congratulations. You obviously don’t need to print out Bayes’s theorem and attach it next to your monitor (plus, you’ve successfully beaten some very nasty tendencies of human reasoning, the prevalence of which has been well-established through psychological research). Others, like myself, might however benefit indeed from drawing more consciously on Bayes’s theorem when developing our arguments (at least for ourselves, whether it is productive to do so in writing is a different question, to be sure) because mistakes in these areas automatically imply rather fundamental problems for our conclusions.

So I think I largely agree with the rather limited role Given wants to assign to Bayes’s theorem for the process of biblical research. My point simply is that it comes into play at a very foundational level of the construction of exegetical arguments – and that disregard for the methodological principles as they can be developed on the basis of Bayes’s theorem are more often neglected by exegetes that we might want to assume.

4. Bayesian Reasoning Does Not Offer “Objective Numbers” as Opposed to “Subjective Opinions”

After having addressed the potential benefits from familiarising oneself with Bayesian reasoning for biblical studies, let’s now turn to some limitations that Given correctly identifies:

“It must be acknowledged that the vast majority of historians do not employ Bayesian probability theory, and for good reason. Bayesian theory works best with large and well circumscribed data sets of various kinds, such as doctors evaluating test results on the basis of copious previous patient statistics—and I would much rather be diagnosed by a doctor who understands Bayesian probability theory than one who does not! Further, I can certainly see how Bayesian theory could be useful in sociological research where large amounts of statistical data are available. However, even though Heilig acknowledges the problem (e.g., 34–35), I do not think he really takes seriously enough how little data we are actually working with when trying to determine Paul’s intentions regarding Rome. One has only to observe how the same small handful of relevant texts from the letters keep coming up again and again in the course of the book to be reminded of this. These letters are an incredibly small sampling of the life of Paul of Tarsus, and when one considers the rhetorical and situational nature of every one of them, the confidence that probability theory can contribute substantially to this sort of historical problem seems misplaced. Heilig says, ‘There is no result that is better than the best, and Bayes’s theorem is a valuable guideline in reaching it’ (35). When dealing with fragmentary data from two millennia ago, almost always open to multiple interpretations, this sort of scientistic reasoning is problematic. The best result is the most accurate result, and Bayesian reasoning based on limited data might actually undermine it.”

I fully agree with almost everything Given says here. In fact, I still believe that I’ve said some of these things myself in Hidden Criticism?, though probably not clearly enough. For example, I write:

“[I]t is clear that often we will not be able to give precise absolute numbers. However, this is not a problem, as long as we can compare different hypotheses relatively to each other.”

Hidden Criticism, p. 34

I should have said: “It is clear that we will almost never be able to give precise absolute numbers” for prior-probabilities or likelihoods! In fact, I never do so in Hidden Criticism. Not even in Paul’s Triumph do I offer likelihoods in relation to the use of θριαμβεύειν for the different suggested senses, even though we have more statistical data in the area of lexicography than almost anywhere else in the realm of historical studies. I would indeed strongly discourage anyone from such attempts. The few I’ve seen are rather embarrassing.

The point about Bayes’s theorem offering access to the “best” possible result should not be mistaken as a reference to precision but to completeness of evidence taken into account. To formulate it more clearly this time: if we are comparing two hypotheses in light of some new evidence and we can’t tell which of the two had been more plausible before the new evidence emerged (prior-probability) and if we can’t tell which of the two hypothesis makes the evidence more predictable (likelihood), we simply can’t say anything about which of the two hypotheses is more probable (“probable” refers here to the subjective “confidence in the truth of  [the hypothesis] H. How much would you be willing to bet on the truth of H?”, Hidden Criticism, p. 28).

In such a situation, we shouldn’t complain that Bayes’s theorem somehow is unhelpful nor should we elevate the one aspect that we perhaps can evaluate to the status of being the decisive factor in deciding which hypothesis is more probably true. Intuitively we might know that this is not a good procedure, Bayes’s theorem even tells us that this is outright impossible.

This does not mean, by the way, that we can’t “do” anything with a hypothesis unless we can make assessments of likelihoods and prior-probabilities in comparison to alternative hypotheses. We can, for a start, still do research on the two aspects and work towards that goal. Also, even if that goal is unattainable, this does not mean that we are not allowed to “accept” one of the hypotheses. Bayes’s theorem needs to be consulted in order to determine which hypothesis is most probable in light of certain evidence. Whether you should accept the hypothesis that is more probable in light of the current evidence and whether you can only accept hypotheses that can be designated as probable is an entirely different (research-pragmatical and even “ethical”) question. I didn’t write a lot about this in Hidden Criticism, mostly, I have to admit, because my wife Theresa had not yet helped me to understand this difference between probability assessment and hypothesis choice sufficiently. You can now read more on this in our chapter on “Historical Methodology,” which is available for free here.

5. Outlook: How I Teach Bayesian Reasoning in the Context of Biblical Studies

In closing, I would like to point out how I’ve come to introduce the concept of Bayesian reasoning to my students recently. It develops the basic thought of the video that I linked to above but makes use of actual events in the recent past. Perhaps it’s also useful for you:

Imagine that it’s Election Night 2016. Assuming that you trust mainstream media, you are quite certain that Hilary Clinton is going to win. If you’d be forced to attach a number to your certainty, you might perhaps refer to various predictions, ranging from a 71% to a 98% chance for Hilary’s win (with Trump’s chances being somewhere between 2 and 29%). The quite influential number by the New York Times suggested an 80% chance of winning at election day.

This kind of expectation is called “prior-probability” in Bayesian terminology.

So now imagine you were hit by a truck before the results were coming in. You wake up several weeks later in the hospital, with the first words you are hearing on TV being that the president just issued a “travel ban” for Muslims. You don’t know yet what the name of the new president is but you will immediately begin to adjust your expectation for who probably won the election. How do you do that? You assess what is called the “likelihoods” of hypotheses (i.e., confusingly, the probability of the evidence dependent on the hypothesis) in Bayesian terminology, i.e. you try to answer the question of how predictable the observed event (“travel ban”) would be if Trump or Clinton had won the election.

Now, we haven’t witnessed several presidencies by these two persons, so we don’t have a statistical value we can use to say how frequently in hundred presidencies they would do such a thing. Our situation is quite similar to the historian of the more distant past. It’s arguably not impossible that given certain events Clinton might have done something similar. So P („travel ban“ │Clinton) – the probability of a travel ban if Clinton were president – is certainly not zero, even though probably close to it. On the other hand, Trump had promised so much on the campaign trail that one might deem it unreasonable to expect that he would be implementing every bit of his agenda once elected. So on the other hand P („travel ban“ │Trump) is also not unity, even though it will probably be much higher than the Clinton-value.

Thus, in any case, these likelihoods seem to “favour” a Trump-presidency. In other words: the prior-probabilities from election night (i.e. your expectations before you heard of the travel ban) need to be adjusted – and a shift of some degree towards the hypothesis of a Trump-victory will occur.

Now, Bayes’s theorem tells us exactly how we are supposed to do that. Our final verdict, the “posterior-probability” will vary, to be sure, depending on how we answer certain questions:

  • Which one of the prior-probabilities do we choose? Which poll do we rely on? Perhaps we’ve been convinced of the existence of the “hidden Trump voter” all along?
  • How probable is it that Clinton would do something that would be described as a “Muslim travel ban” on TV?
  • Again, we might ask more specifically: how reliable is TV coverage anyway? Perhaps they are largely overstating what Clinton might have intended?
  • Also, how unprecedented would such a move actually be for a democratic president?
  • And anyway: politicians change their position all the time, right? Like Angela Merkel’s energy policy changed  180° immediately after the Fukushima catastrophe. Perhaps there was a new terrorist attack, which influenced public opinion? 
  • Also, how certain is it in any case that Trump would carry through a conservative agenda after being elected president? Hasn’t he been a democrat for quite some time?

So the combination of traits of a fervent Hilary supporter with little trust in the media (“They are the ones who created Trump!”) might, for example, result in the situation that he or she would still believe that Hilary probably won the election. In other words: the posterior-probability of Hilary’s victory might still be greater than 0.5 from the perspective of such a person.

Note that this posterior-probability can then be treated as the prior-probability of a renewed updating cycle, once new information becomes available (e.g. the phrase “president Trump”). (This is why some Bayesianists will tell you that the initial priors actually don’t matter at all.)

It’s actually quite fun playing with the numbers in the classroom and fascinating to see how different combinations of answers result in very different results. But of course, I won’t do so (here). Because the whole point of this post is, after all, that it’s not primarily about the numbers.

Rather, in the context of the potential use for biblical studies, it is all about, for example becoming aware of the fact that we often come to a hypothesis with some prior notion about its plausibility in comparison to alternatives. Even if we didn’t trust polling data at all (or somehow had been blissfully unaware of it on election eve), we would probably still have expected one candidate to be the more plausible winner. Or we might have actually thought that the chances were 50:50. In this case, the new evidence, the talk about a travel ban for Muslims, will necessarily tip the scale, i.e. the hypothesis favoured by the comparison of likelihoods will be the one with the greater posterior probability.

Also, it’s about recognising how new evidence alters our prior notions of plausibility – and that this new plausibility is not (!) simply identical with how well the new evidence can be explained … for the old prior-probability gets updated – but not simply discarded. If we tried to convince our roommate that Trump “has” to be the new president because it’s more probable that he and not Hilary would have signed such a declaration, we could only hope that he or she had never heard of Bayes’s theorem before. (Again, does this not sound familiar at all to you?)

So that’s the take-away from this post: Bayes’s theorem offers a wonderful opportunity for dissecting political discourse in the classroom – and it might also improve our perception of scholarly discourses on the biblical texts and the way we construe our own exegetical arguments.

6. For Further Reading:

  • On historical methodology and the use and misuse of confirmation theory (Bayesian reasoning) and abduction (inference to the best explanation) see this essay that I wrote together with Theresa Heilig.
  • For a demonstration that we more often disregard the methodological principles that can be developed on the basis of Bayes’s theorem (but no doubt also accepted without ever consulting mathematical expressions), see my book Paul’s Triumph. For more information, see here. For a recent review in RBL, see here.
  • My very first attempt of dealing with Hays’s criteria from a Bayesian perspective can be read here fore free.
  • For an example on how exegetical arguments follow Bayesian lines of thought – and diverge from it sometimes – see my recent article (also available for free here) on the Antioch incident and the NPP (even though I have to add that I would put some things differently now; the article was in the editorial process for several years).
  • Some years ago I also wrote an article for the Freiburger Zeitschrift für Philosophie und Theologie, in which I demonstrate that a variation of the Intelligent Design-argument as it is common in the German sphere has to be judged incomplete against the backdrop of Bayes’s theorem. You can read the article (in German) for free here. Some of the considerations can also be applied to the analysis of discourse among biblical scholars.

Christoph Heilig is the author of Hidden Criticism? (Fortress, 2017) and Paul’s Triumph (Peeters, 2017).

This research has recently received the Mercator Award in the Humanities and Social Sciences.

Additionally, he has co-edited (with J. Thomas Hewitt and Michael F. Bird) God and the Faithfulness of Paul: A Critical Examination of the Pauline Theology of N. T. Wright (Fortress, 2017). 

In his most recent – and voluminous – project, which has just been completed, he discusses the importance of “stories” and “narrative substructures” for understanding Paul’s letters.

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