## The Criteria For Interpolation: Using Bayes To Evidence Authenticity

14 Sep

In a previous post I went over what I think is an application of sliding the probability one way or another in favor of interpolation based on the criteria I listed (manuscript, anachronism, vocabulary/linguistic, contextual, and doxological inconsistency).

Some people might think that it was unfair that I started with the priors that I did. However, I want to show that, using Bayes Theorem, we can use it to demonstrate a very low probability of interpolation in a separate section using the same priors.

Instead of Romans 1.2-6, let’s say I used a random section like Romans 2.2-6, which is this block of text:

2 Now we know that God’s judgment against those who do such things is based on truth.3 So when you, a mere man, pass judgment on them and yet do the same things, do you think you will escape God’s judgment?4 Or do you show contempt for the riches of his kindness, tolerance and patience, not realizing that God’s kindness leads you toward repentance?5 But because of your stubbornness and your unrepentant heart, you are storing up wrath against yourself for the day of God’s wrath, when his righteous judgment will be revealed.6 God “will give to each person according to what he has done.” (Psalm 62:12; Prov. 24:12 )

Again, because of Marcion, there is a precedent for general interpolation (verse 6 quotes the LXX which Marcion probably would not have tolerated, and the entire context that this section belongs to speaks about the judgement of Paul’s god). Yet again, there is no manuscript evidence that this section is missing.

Now, is there any linguistic evidence for interpolation? As far as I can tell, all of the vocabulary used by Paul here is vocabulary that he has used elsewhere. And we would expect the original author to use the same vocabulary, so as I wrote in that previous post, based on the conditionals that I outlined, this lack of linguistic inconsistency is strong evidence in favor of originality:

Priors:
Probability of Authenticity P(H) = .6
Probability of Interpolation P(~H) = .4
Conditionals:
Probability of the same vocabulary given authenticity: P(E | H) = .7
Probability of the same vocabulary given interpolation: P(E | ~H) = .3
Revised:
P(H | E) = P(E | H) * P(H) / [P(E | H) * P(H)] + [P(E | ~H) * P(~H)]
P(H | E) =  .7 * .6 / [(.7 * .6) + (.3 * .4)]
P(H | E) = .7778

This moves the prior probability of 60% to the revised probability of 78%.

I should note that I picked the conditionals that I did because most scholars would agree that Paul using the same vocabulary given a passage’s authenticity is a very persuasive argument. Likewise, the interpolator using the same vocabulary as the original Paul given an interpolation is proportionally unpersuasive. Like I wrote in the previous post, some scholars consider the arguments I listed for interpolation unpersuasive (at Romans 1.2-6), but even given the unpersuasiveness of the evidence presented, it should still be allowed to slide the probability in favor of interpolation. The amount that one allows it to slide is what is meant by persuasive or unpersuasive.

Now what about the second line of evidence I posted, linguistic/contextual? Again, this section seems to fit word use that Paul always uses in similar contexts. We would expect exactly this, so this is more evidence in favor of authenticity:

Priors:
Probability of Authenticity P(H) = .78
Probability of Interpolation P(~H) = .22
Conditionals:
Probability of vocabulary used in a similar context given authenticity: P(E | H) = .7
Probability of vocabulary used in a similar context given interpolation: P(E | ~H) = .3
Revised:
P(H | E) = P(E | H) * P(H) / [P(E | H) * P(H)] + [P(E | ~H) * P(~H)]
P(H | E) =  .7 * .78 / [(.7 * .78) + (.3 * .22)]
P(H | E) = .8909

This moves the prior probability of 78% to the revised probability of 89%.

The third line of evidence, this section being larger than what Paul usually writes in an introduction? Since this is not an introduction, it does not seem applicable. Since it is not evidence either way, it gets a 50/50 chance; that is, it is not evidence of anything so the prior does not change.

Priors:
Probability of Authenticity P(H) = .89
Probability of Interpolation P(~H) = .11
Conditionals:
Probability of section size given authenticity: P(E | H) = .5
Probability of section size given interpolation: P(E | ~H) = .5
Revised:
P(H | E) = P(E | H) * P(H) / [P(E | H) * P(H)] + [P(E | ~H) * P(~H)]
P(H | E) =  .5 * .5 / [(.5 * .89) + (.5 * .11)]
P(H | E) = .89

Lastly, I posited theological inconsistency as a marker for interpolation. The theology here (the judgement of Paul’s god) seems to fit Paul’s theme of judgement. And again, this is exactly what we would expect, so this is more evidence in favor of authenticity.

Priors:
Probability of Authenticity P(H) = .89
Probability of Interpolation P(~H) = .11
Conditionals:
Probability of theological consistency given authenticity: P(E | H) = .7
Probability of theological consisency given interpolation: P(E | ~H) = .3
Revised:
P(H | E) = P(E | H) * P(H) / [P(E | H) * P(H)] + [P(E | ~H) * P(~H)]
P(H | E) =  .7 * .89 / [(.7 * .89) + (.3 * .11)]
P(H | E) = .9501

This moves the prior probability of 89% to the revised of 95%.The thing that I was hoping to demonstrate here is the fact that Bayes Theorem, if graphed as more evidence is gathered, would produce an asymptote. That is, we can keep gathering evidence all day, but it will never reach 100%. More and more evidence continues to slide the probability towards 1, but it will never reach 1.

1 Comment

Posted by on September 14, 2011 in Bayes

### One response to “The Criteria For Interpolation: Using Bayes To Evidence Authenticity”

1. September 15, 2011 at 1:24 am

Thanks for posting this. It was a good illustration of the process.

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