The Criteria For Interpolation: More Examples of Bayes Theorem in History

13 Sep
One of the problems we encounter when we start doing critical analysis of the NT is that there is always a threat that what we are reading was not penned by the original author. Sometimes it is an honest mistake; a scribal note inserted into the body of a text by a later copyist (probably what happened with Josephus’ reference to Jesus in AJ 20.9.1). Other times, it is an insertion into a text done to promote a particular dogma; using the authoritative voice of antiquity to argue for an interpolator’s point of view.

So we have to have a methodology for seeing what the original author wrote and what a later author put into the original’s pen. But we have to be careful of wantonly chopping up and removing certain sections of an ancient work we are reading without reason.

Interpolations can be suggested and argued by positing a range of criteria. If a passage is anachronistic (like 1 Thessalonians 2.13-16), then there is a high probability that it is an interpolation. If there is manuscript evidence for a passage being all over the place (like John 7.53 – 8.11) or is not in some of the earliest manuscripts (like Mark 16.9-20) then this is also a high probability indicator of interpolation. But once we start talking about “probability”, at least to me, we are starting to get into the realm of Bayes. Here is a post I made over at Vridar:

The case for interpolations should be approached in a Bayesian way. Linguistics, manuscripts, context, theology, anachronisms, etc. can all be added together to make a case. If there’s no manuscript evidence but there’s linguistic, contextual, anachronistic, and theological inconsistency, then a case can be made for interpolation in a Bayesian sense. All it really means is that each one of those indicators slides the probability towards it being an interpolation. It shouldn’t be an “either-or” methodology; it should be about probability.

For something like the collection of Paul’s letters, there is already a precedent for general interpolation: Marcion was the first Christian to promulgate Paul’s letters as an authoritative canon for Christians. Yet, his theology and Christology was antithetical to the emerging Catholics. Thus Paul’s letters in Marcion’s canon could not be word-for-word the exact same ones that are in the current NT; the NT that the Catholics put together to combat Marcionism (i.e. Catholics followed the same “gospel-apostle” set up for the order of books in their/our Bible that Marcion created).

There can be very little doubt that Marcion removed some passages from Paul. But since no one quotes Paul prior to Marcion, how do we know whether the proto-Catholics published the “originals” or whether they added to Marcion’s Paul to combat Marcion? (The presence of Marcionite prologues to Paul’s letters in Catholic Bibles is evidence of the latter)

So I’ll use Romans 1.2-6 for a case study in interpolations using Bayes Theorem.

The only time Paul ever uses the phrase “holy scriptures” (γραφαις αγιαις [pl. dat.]) is in Romans 1.2 and 2 Timothy 3.15. Since 2 Timothy in its entirety was not written by Paul, this could be linguistic evidence that Paul did not write Romans 1.2. Of course, there is more linguistic and even Christological/dogmatic (i.e. anti-Marcionite) evidence for this, so in a Bayesian sense, based on 2 Tim, there is a high probability that Romans 1.2-6 was not written by Paul.

Of course, some scholars do not consider these arguments persuasive. Again, this seems like a problem for Bayes, since Bayes Theorem is designed to include all other interpretations of the evidence before sliding the prior probability one way or another. In other words, the pseudo-Pauline author of 2 Tim using “holy scriptures” is linguistic evidence for Romans 1.2 being authored by the same person as 2 Timothy; it might be strong or weak evidence but it is evidence nonetheless. It could also be evidence that the author of 2 Tim is emulating the original language found in Romans 1.2 (but we have no evidence for this; the entire reason that 2 Tim is thought to not be written by Paul is due to linguistic evidence). Again, deciding between each hypothesis would be a problem for Bayes Theorem to solve as we gathered more evidence in favor of one or the other.

Bayes Paves The Way

So I listed above in the quote five markers for possible interpolation: manuscript, linguistic/vocabulary, contextual, anachronistic, and theological (or doxological or Christological) inconsistency. In the case of Romans 1.2-6 we have linguistic and doxological evidence in favor of interpolation, yet manuscript evidence for originality (there are no extant manuscripts of Romans without 1.2-6).

The problem, of course in Bayes theorem, is deciding what priors to use. There is already a precedent, due to Marcion, that the introduction of Romans was not written by Paul (verses 2-4 are very anti-Marcionite). Yet, the strongest indicator – manuscript evidence – is not apparent. So to be fair, I think I will set the prior for interpolation, due to lack of manuscript evidence, at 40% (i.e. the fact that all manuscripts have this introduction is 60% evidence in favor of originality). Let’s see where this takes us as we gather and analyze more evidence.

First, what would we expect if there was linguistic evidence for interpolation? The writer would use vocabulary that Paul himself never uses. We have exactly that with the presence of “holy scriptures” in Rom 1.2. But it seems as though it could go either way, like I wrote above (interpolator could either be emulating Paul’s original language, or interpolator could be inserting his own terms). What tips the scales, for me, is that Paul nowhere else uses the term “holy scriptures” in his authentic writing, always saying “as it is written” (καθως γεγραπται*) or simply “scriptures” without the qualifier “holy”. So the presence of “holy scriptures” in Romans most certainly would not be evidence in favor of authenticity; I would have this conditional probability at 55% in favor vs 45% against. This moves the prior probability from 40% to the posterior probability of 45%.

 Hypotheses: Prior Probabilities: Revised Prob:

Notice, however, that if I were positing an interpolation but the language was the same, I think it would be a horrible argument or very bad evidence for interpolation:

 Hypotheses: Prior Probabilities: Revised Prob:

There is a very high probability that original author would use the same language that he uses throughout the rest of his letters. We would not expect the interpolator to do so; only highly skilled redactors who are trained to look for that sort of thing would be able to pass off a sophisticated interpolation, which I’m guessing was not a very common skill in the 2nd century (though Richard Carrier, an expert on the ancient Greco-Roman world, says that there must be sophisticated interpolations that we cannot detect).

So now our prior probability becomes 45% as we continue to add more arguments/evidence.

As I wrote in that previous post, the instance of “holy scriptures” is not the only evidence in favor of interpolation. Paul never talks about “prophets” in the context of prophets of the Hebrew bible. He always mentions prophets in conjunction with apostles. In other words, Paul overwhelmingly talks about contemporary prophets in his letters. And when he actually quotes from a book of the Nevi’im, he always says καθως γεγραπται[*]. Romans 1.2 is the only time he writes about long-dead prophets predicting Jesus. Again, this is very weak evidence, but it is evidence nonetheless. I think it might be fair to move the two conditional probabilities closer to 50% in my estimation:

 Hypotheses: Prior Probabilities: Revised Prob:

The strongest argument, to me, is the fact that this introduction in Romans is longer than every other Pauline letter – even the contested and pseudonymous ones. Much more so because Paul never goes over doxological statements in any other introduction. This is much stronger evidence for a non-Pauline hand writing this section:

 Hypotheses: Prior Probabilities: Revised Prob:

Now our prior has moved to the posterior of 56% in favor of interpolation. Notice again, to be fair to the opposing hypothesis, that if I were positing an interpolation – even with all of that prior evidence that we already had – it would be a bad argument for interpolation if this section was the same length as all other Pauline introductions:

 Hypotheses: Prior Probabilities: Revised Prob:

We would most certainly expect this introduction to be the same length as all other introductions if there was no interpolation. By necessity, it would be impossible to have an interpolation if it was the same short length as all other Pauline letter introductions. All interpolations add text; that is sort of the definition of an interpolation.

For my last line of evidence, we have a Christology at Rom 1.6 that seems to contradict the Christology of the Phillipian Hymn (Phillipians 2.5-11). The Phillipian Hymn, according to many scholars, is a pre-Pauline hymn that Paul is quoting from. This hymn assumes the same sort of Christology that the opening line of the gospel of John assumes: That Jesus was equal to god and descended from heaven even though he had equality with god (Phil 2.6, compare Jn 1.1-2). However, Rom 1.6 says that Jesus was declared son of god due to his resurrection. This implies to me that Jesus prior to his resurrection was a normal yokel, none of that “in the form of” and “equal to” god stuff; it implies an adoptionist Christology.

But it could go either way. Since Paul did not actually compose the Phillipian Hymn, and it has a parallel to other Christian writing, it would hardly be fair to call this hymn an original thought of Paul. So while I posit it as evidence, it is probably very weak evidence in favor of interpolation.

 Hypotheses: Prior Probabilities: Revised Prob:

This move the prior probability of 56% in favor of interpolation up a bit to 57%.

Again, all of this Bayesian analysis depends on the priors. If I had picked completely skewed priors (like 10% in favor of interpolation, or 90% in favor of interpolation) then that would poison the well so to say and we could never get a reasonable answer. I also attempted to pick conditionals that were pretty close to each other as well, since skewing there would have a similar effect. I even picked extremely low conditionals to be fair to those scholars who might find such evidence unpersuasive. “Persuasive” really just means “high probability” in the context of Bayes Theorem. If something is unpersuasive, it would probably be something under 55% probable. Even with the addition of “unpersuasive” evidence (like the ridiculously low 51% conditionals that I added), accumulated we still have above a 55% chance that Romans 1.2-6 is not original to Paul. The final posterior probability might be much higher than 57% if I had used more reasonable numbers.

Explanation of Conditionals

If I had conditionals that were equal, say at a 50:50 ratio, then this means that some evidence I have posited is not really evidence for anything at all. Any time a conditional is presented as evidence for something, it has to be over 50% (when there are only two competing hypotheses). This means that the ratio of evidence against has to equal 100% when the two are added together. For example, the long introduction in Romans certainly would not be presented as evidence for authenticity; it is either strong or weak evidence against authenticity… but evidence nonetheless.

For a more modern example, let’s say someone was killed between the hours of 2am – 4am this morning. I personally do not have an alibi for these two hours, so it would be evidence in favor of me being the murderer. But this is very, very weak evidence since there are not any other reasons why I would murder someone without some other corroborating evidence to give it relevance. How many other hundreds of thousands of people have no alibi for that time period? On the other hand, my not having an alibi at this time period most certainly would not be touted as evidence for my innocence. So it is very weak evidence for me being a murderer to the point of insignificance, but never evidence for my innocence.

So this is why all of the evidence I posited was above 50% in my conditionals.

This, to me, is another good reason to use Bayes Theorem for arguments. Even if we have multiple unpersuasive arguments in favor of something, that accumulation is the actual strength of the argument, not the individual components. One of the best arguments for the Theory of Evolution is not each individual example of evidence, but the accumulation of all of those different lines of evidence that best supports the ToE; the reasoning behind Bayes Theorem is why the ToE is more likely correct than incorrect. Just like Bayes Theorem demonstrates above (hopefully!) that Romans 1.2-6 was not originally written by Paul. Creationists can assign 51% (i.e. unpersuasive) to each and every line of evidence in favor of evolution – their Bayesian accumulation will still be overwhelmingly in favor of evolution. Moreover, the Creationist has to come up with mutually exclusive alternative explanations for each and every line of evidence, which means that their explanations are not cumulative in a Bayesian sense; the Theory of Evolution is one theory that explains all of the accumulated evidence.

In a future post I’ll go over the problem that religionists have when positing their religion as an explanation for phenomena, since probability theory deals a pretty significant blow to their explanatory power (or, when you do not necessarily have to use Bayes Theorem in assessing probability).

[*]Rom 1.17; 2.24; 3.10; 4.17; 8.26; 9.33; 11.26; 15.3, 9, 21; 1 Cor 1.31; 2.19; 10.17, 2 Cor 8.15; 9.9

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Posted by on September 13, 2011 in Bayes

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