Venn Diagrams and the Synoptic Problem

I mentioned that I gave a paper in Oslo some weeks ago on the issue of manuscripts and the synoptic problem. While it was the issue of manuscripts and variant readings that was the focus of my attention, writing this paper forced me to revisit some foundational scholarship on the gospels and challenged me to try to visualize some data for a general audience. I did so using Venn Diagrams. Now I see that Mark Goodacre, in a series of posts (here, here, and here) prompted by the insightful work of Matthew Larsen, has also been experimenting with Venn Diagrams to model synoptic relationships (see also the interesting contribution by Joe Weaks).

While Goodacre has been mainly working with relationships between two gospels, I wanted to try to model all three synoptic gospels together using such a graphic. I discovered, however, that you can’t really represent things quite accurately with three circles. To get the model to fit the data, you would need shapes other than perfect circles (this would be a Euler Diagram). So instead of perfect representation, I have chosen to stick with the Venn Diagram (albeit a rough one) to try to model the overlap of the three synoptic gospels.

I should also note that I used a different source of data from that used by Larsen and Goodacre. Rather than counting stories in the Nestle-Aland Synopsis, I relied on the word counts in the old study by A. M. Honoré, “A Statistical Study of the Synoptic Problem,” Novum Testamentum 10 (1968), 95-140. Using those numbers (which differ in that they more nearly indicate the relative length of the gospels and show Luke preserving a bit less of Mark), I came up with this rough diagram:

Venn Diagram Scaled 1Now, the most widely held “solutions” to the Synoptic Problem is the so-called “Two  Source Hypothesis” (or “Two Document Hypothesis”), which, in the words of John Kloppenborg, can be summarized as follows:

“Stated succinctly, the Two Document hypothesis [2DH] proposes that the gospels of Matthew and Luke independently used Mark as a source. Since Matthew and Luke share about 235 verses that they did not get from Mark, the 2DH requires that they had independent access to a second source consisting mainly of sayings of Jesus. This, for want of a better term, is the ‘Sayings Gospel,’ or, ‘Q’” (John S. Kloppenborg Verbin, Excavating Q: The History and Setting of the Sayings Gospel [Minneapolis: Fortress Press, 2000], 12-13).

One of the reasons I wanted to stick with the circles in the Venn Diagram is to illustrate a particular point about the Two Source Hypothesis. If we color the circles in a way that highlights the material in the so-called “Q-Source” (the material common to Matthew and Luke but not present in Mark), we can see this segment quite clearly:

Venn Diagram Scaled Q 1

One of the main problems for proponents of the Two Source Hypothesis is the existence of agreements between Matthew and Luke against Mark. According to the Two Source Hypothesis, this shouldn’t happen (Matthew and Luke are said to have used Mark independently of one another; so agreements between them against Mark should be rare or non-existent). Some proponents of the Two Source Hypothesis try to explain some of these agreements by suggesting that there was some “overlap” between Mark and Q, and that Matthew and Luke have sometimes chosen the Q version of a passage or phrase insead of the Markan version. They call such material Mark-Q overlaps, or something similar. So here is where I think our Venn Diagram becomes useful. If we adjust it to allow for overlap between Mark and Q, we can see what happens:

Venn Diagram Scaled Q 3

The more Mark-Q overlap we allow, the more Q begins to look like Matthew (and, to a somewhat lesser extent, like Luke). The more Q looks like Matthew, the less Q seems to be a necessary hypothesis, and the more it seems like the Farrer-Goodacre Hypothesis (Markan priority without Q) seems to be the more viable solution to the synoptic problem.

This point has of course been noted by many students of the synoptic problem, but I think the Venn Diagram really vividly illustrates the idea and helps it to sink in.

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17 Responses to Venn Diagrams and the Synoptic Problem

  1. Many thanks, Brent. Enjoyed the post and the diagram, and it’s a great point about the Mark-Q Overlaps. Of course one might also bleed some green into that triple tradition section too, bearing in mind Sanders and Davies’s point that there is not a single triple tradition pericope that lacks a minor agreement, and my point (if I may be so bold!) that some of the supposed triple tradition pericopae with minor agreements actually have more Matthew-Luke agreement than do some of the supposed Mark-Q Overlap pericopae.

    My only question on the diagram is that the double tradition section looks larger than the triple tradition section. Shouldn’t triple be almost twice as big? (Honore’s triple tradition has 8336 / 8630 / 7884 compared to his double tradition at 4461 / – / 4476).

    • Thanks, Mark. Yes, you’re quite right about the double tradition / triple tradition distortion. This is one of the features that is difficult to handle when using circles rather than other more irregular shapes. I wasn’t able to find a good online tool for generating a Euler Diagram from the kind of data that Honoré provides.

  2. Timothy Joseph says:

    The Venn diagram is a great tool to illustrate your point! Those of us who hold the priority of Matthew’s account would point out that Mathew contains all of the mysterious Q and most of Mark.


  3. Ron Price says:

    May I suggest that if we look into the various areas in your second Venn Diagram, there is a clue to the solution to the synoptic problem. For the area which you referred to as ‘Mark-Q overlap’ is the only one in which the the text consists almost entirely of aphorisms (c.f. Fleddermann, ‘Q: A Reconstruction and Commentary’, pp.75-76). The other areas (except perhaps the very small ones) contain text with mixed literary styles. This would be explained if we posit that all three synoptic writers were making use of a written source containing aphorisms, that Mark was more selective than Matthew and Luke, and also that he generally preferred to shorten, or even exclude longer aphorisms such as the advice not to worry, the warning about seeking a sign, and the woes to Pharisees. The non-aphoristic pericopes in the double tradition can be explained as Luke copying from Matthew or vice-versa.

  4. Thanks, Brent. I suppose that goes to Joe Weaks’s point about the greater ease of working with rectangles.

  5. “For the area which you referred to as ‘Mark-Q overlap’ is the only one in which the the text consists almost entirely of aphorisms.” The Mark-Q overlaps include all that material from Matt. 3-4 // Luke 3-4 (John’s Preaching, Temptation, etc.), as well as Beelzebub, right?

    • Ron Price says:

      I’m not sure what you mean by “all that material”, Mark. I concede that Fleddermann’s list of ‘Mark-Q overlaps’ does indeed include Mk 1:7-8 and parallels which is arguably not an aphorism, and Mk 3:22-27 and parallels which is certainly not an aphorism. But this is only two texts in a list of 28 overlap texts.

      • Thanks, Ron. Streeter (Four Gospels, 305-6) suggested that there were six “Mark-Q Overlap” passages:

        (1) John the Baptist (Matt 3.1–12 // Mark 1.1–8 // Luke 3.1–18)
        (2) Baptism of Jesus (Matt 3.13–17 // Mark 1.9–11 // Luke 3.21–22)
        (3) Temptation (Matt 4.1–11 // Mark 1.12–13 // Luke 4.1–13)
        (4) Mission Discourse (Matt 10.5–15 // Mark 6.6b–13 // Luke 9.1–6 // Luke 10.1–12)
        (5) Beelzebub Controversy (Matt 12.25–32 // Mark 3.23–30 // Luke 11.17–23, 12.10)
        (6) Mustard Seed (Matt 13.31–32 // Mark 4.30–32 // Luke 13.18–19)

        Here, the text clearly does not consist “almost entirely of aphorisms”.

  6. One more comment, if I may, on re-reading your post:

    “I should also note that I used a different source of data from that used by Larsen and Goodacre. Rather than counting stories in the Nestle-Aland Synopsis, I relied on the word counts in the old study by A. M. Honoré . . . . Using those numbers (which differ in that they more nearly indicate the relative length of the gospels and show Luke preserving a bit less of Mark) . . . ”

    Those Honoré numbers are also effectively “counting stories”; it’s just that he’s using a different Synopsis, Huck’s, and counting the number of words within those stories. They are a touch more precise on the relative length of the gospels, agreed, but they only show Luke preserving less of Mark because Huck’s Synopsis is more restrictive in counting Lucan parallels than Aland’s.

    • Thanks, Mark. Agreed on all counts. In looking at Joe Weaks’ excellent diagrams, I see that my Mark circle is out of proportion with the Matthew and Luke circles, causing some of the problems in my diagram. With regard to Huck’s Synopsis being “more restrictive in counting Lucan parallels”: This is the kind of thing that really interests me. Some of the different text critical decisions in Huck and Aland really do matter for synoptic problem questions. When you get down to the level of determining agreements between Matthew and Luke against Mark, the small textual changes can (cumulatively) make a big difference. And there are some truly interesting examples. I’m fascinated with Matt. 12:8 // Mark 2:28 // Luke 6:5 in these two synopses. In fact, that might get its own post.

  7. Thanks, Brent! Agreed on the importance of text-critical decisions for Synoptic questions. But also, one of the issues with the Synopses is that they were constructed by people who took the independence of Matthew and Luke for granted (Huck, Greeven, Aland), and to that extent, they sometimes represent the data in ways that play to that.

    I’d love to see your reflections on Matt. 12:8 // Mark 2:28 // Luke 6:5!

  8. Ron Price says:

    Mark, I’m surprised you think that the assessment by Fleddermann to which I referred is trumped by an assessment by Streeter, whose analysis of ‘Mark-Q overlaps’ was published over 80 years before Fleddermann’s. Of your six texts, (2) is not certainly in Q, and (4) and (6) are aphorisms. This leaves three texts which are not aphorisms. As against this, apart from Mk 1:2 (counted separately), Fleddermann’s list contains 26 aphoristic texts.
    So in the absence of a convincing case against Fleddermann on this point, I stick to my claim that the overlap between Mark and the double tradition consists almost entirely of aphorisms.

  9. Pattycake says:

    Is this showing that all of Q is in Matthew?

    • Well, Q is by definition the material that is present in both Luke and Matthew but absent from Mark. So all of Q that “survives” is in both Luke and Matthew. Presumably advocates of the Two-Source Hypothesis would say that there are some parts of Q that were left out by both Luke and Matthew, but when we’re talking about the possible lost contents of a hypothetical document, we’re not so far from asking how many angels can dance on the head of a pin.

      • Pattycake says:

        I see. Why do some scholars think that Q predates Mark?

      • I’m not sure. Perhaps they think it is more “primitive” in some respects? It’s a difficult question. Not only is Q hypothetical, but our knowledge of the date of the composition of Mark is also quite shaky.

  10. Brent, not sure how handy or timely may be, but there are at least a few R packages that purport to draw Euler diagrams reasonably well. The most promising looking one (to my eye) is the package “eulerr”, and it looks like it does ellipsoid -grams, but maybe not rectangular ones. A sample page from the manual with pics here

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