Showing posts with label statistics and the synoptic problem. Show all posts
Showing posts with label statistics and the synoptic problem. Show all posts

Tuesday, May 17, 2011

Sharon Mattila's Statistics and the Synoptic Problem: Some Quibbles

One of my favourite spare time activities is to dip into statistical studies of the Synoptic Problem. One day I might even write something about it. In going back over an article by Sharon Lea Mattila recently, I noticed that I had scribbled all over my print copy and that some of my scribblings might usefully be transferred to a blog post lest they get lost.

The article I wish to comment on is Sharon Lea Mattila, "Negotiating the Clouds Around Statistics and 'Q': A Rejoinder and Independent Analysis," Novum Testamentum 46/2 (2004): 105-31.  The article is a detailed, lengthy and frequently polemical response to Charles E. Carlston and Dennis Norlin, "Statistics and Q -- Some Further Observations," NovT 41 (1999), itself largely a response to an earlier article by Mattila.  For an excellent summary of  these and other works on statistical studies of the Synoptic Problem, and for full bibliography, see John Poirier, "Statistical Studies of the Verbal Agreements and their Impact on the Synoptic Problem," Currents in Biblical Research 7 (2008): 68-123.

The gist of the article is that Mattila thinks that Carlston and Norlin have overstated the case that Matthew and Luke preserved the Q sayings more faithfully than the Marcan sayings.  One of the key elements in the article is "an independent statistical analysis" that attempts to avoid what she sees as the flaws in their earlier study.

My comments here relate to difficulties with Mattila's figures tabulated on pp. 125-6 of the article:

(1) Mattila claims to avoid "such pitfalls as including sayings containing words from Scripture" (p. 121) but two of her parallels feature quotations from Scripture:
  • Matt. 10.34-6 // Luke 12.51-53 quotes Micah 7.6
  • Matt. 21.13 // Luke 19.46 is a famous composite quotation of Isa. 56.7 and Jer. 7.11.
(2) Mattila makes the interesting methodological move to count passages normally attributed to Mark-Q overlap as Triple Tradition (p. 122). In some contexts, this could be a strong and defensible move, e.g. it could help us to take seriously the existence of major agreements in triple tradition material, something that has a bearing on arguments for and against the 2ST. However, in this context, in which she is discussing Carlston and Norlin, and dealing specifically with claims about a written Q in comparison with a written Mark, she is potentially transferring material that should be in one table to the other. Four of her Triple Tradition pericopes are in Mark / Q overlap
contexts:
  • Matt. 10.19-20 // Luke 12.11-12
  • Matt. 13.31b-2 // Luke 13.18b-19
  • Matt. 16.6b // Luke 12.1b
  • Matt. 18.6-7 // Luke 17.1b-3a.
It's an important difficulty with the analysis when evidence that belongs on one side of the experiment ends up on the other.

(3) Mattila includes the Lucan woes in her analysis in spite of the fact that they have no parallel in Matthew, and against her stated objective of treating Aland's synopsis divisions as the standard.  She is conscious that this is problematic (p. 121).

(4) This is a point that is rarely treated seriously in statistical studies of the Synoptics.  Parable material occupies an interesting position here in that it is both sayings  material (in attribution to Jesus) and narrative (in form).  Parallel parables appear often to be much less close to one another in wording than is other sayings material. Indeed, they sometimes imitate the way that narrative material appears. Mattila's double tradition table includes four parables across 47 verses of Matthew:
  • Matt. 7.24-27 // Luke 6.47-9
  • Matt. 18.12-14 // Luke 15.4-7
  • Matt. 22.2-14 // Luke 14.16b-24
  • Matt. 25.14-30 // Luke 19.12b-27
Her triple tradition table includes three parables across only 23 verses in Matthew (the second is the Mark-Q overlap parable of the Mustard Seed listed also above):
  • Matt. 13.3b-9 and 18-23 // Luke 8.5-8a and 11-15
  • Matt. 13.31b-32 // Luke 13.18-19
  • Matt. 21.33-40 // Luke 20.9b-15
(5) Unlike Carlston and Norlin, Mattila excludes from consideration speech from characters other than Jesus (John the Baptist, the Centurion, etc.).  I am not sure about this move, especially as they include famous examples of very high verbatim agreement, thereby potentially skewing the figures for the double tradition.

Thursday, November 15, 2007

Mark-Q Overlaps V: the degree of verbatim agreement

This is the fifth in my current series of posts on the Mark-Q Overlaps (so-called), in which I would like to make a new point about the degree of verbatim agreement between Matthew and Luke in the pericope under discussion in the Q Section where I will be presenting, Matt. 3.7-12 // Mark 1.7-8 // Luke 3.7-9, 15-17 (John's Preaching).

5. The Degree of Verbatim Agreement

The point here is a simple one, but it is one that I have not seen anyone else make in discussion of the Synoptic Problem. The degree of agreement between Matthew and Luke in double tradition material is often too high for them to have been copying from another source. John Kloppenborg helpfully draws attention to this "extremely high verbal correspondence . . . in a significant number of instances" (John S. Kloppenborg, "Variation in the Double Tradition and an Oral Q?", ETL 83 (2007), 53-80, 53) including the one currently under discussion:
Matt 6.24 // Luke 16.13 (98%), Matt 12.43-45 // Luke 11.24-26 (93%), Matt 11.20-24 // Luke 10.13-15 (90%), Matt. 3.12 // Luke 3.17 (88%), Matt. 12.27-32 // Luke 11.19-23 (88%), Matt 23.37-39 // Luke 13.34-35 (85%), Matt. 3.7-10 // Luke 3.7-9 (85%).
These figures "are based on the number of common words divided by the total number of Lukan words" (53, n. 1). Kloppenborg helpfully draws special attention to our pericope:
In the last named pericope, Matthew has 76 words in Greek, 61 or 80% of which are identical with Luke in lexical form and inflection. This would rise to 63 or 83% if καρπόν and ἄξιον are included as agreements. Luke's version has 72 words in Greek, 61 or 85% are identical with Matthew, 63 or 87.5% if καρπούς and ἀξίους are counted as agreements. (53)
As Kloppenborg rightly makes clear, "the extraordinarily high degree of verbatim agreement" here makes theories of an oral mediation of such material impossible. And one might add that there are some striking verbatim strings of agreement here, of 12, 12.5, 20 and 24 words. The latter string, of 24 words, is Matt. 3.9-10 // Luke 3.7b-9.

In the handout that I have produced for the SBL session on Mark-Q overlaps where I will present my paper on this, I have produced a synopsis of Matthew, Q (IQP) and Luke on this so that one can see quickly and easily just how much verbatim agreement there is in this passage. Indeed, what is remarkable is how little disagreement there is. I have coloured all the agreement grey, and there is very little white left. One of the reasons for doing this in three columns is to remind ourselves of the fact that on the Q theory, what we have here are triple agreements. We get so used to thinking about this material as "double tradition", in the sense that it is present only in Matthew and Luke among the extant texts, that we can easily forget that for Q theorists, the agreements here are triple agreements, between Matthew, Q and Luke.

This leads us to an interesting question about the degree of verbatim agreement here between Matthew, Q and Luke. Does one ever see this kind of agreement between Matthew, Mark and Luke? Are the triple agreements in Matthew, Mark and Luke similar in extent to the triple agreements between Matthew, Q and Luke? The question that I am asking here is, I think, a new one. If anyone else has asked this question, then I have missed it. The question itself is an important one, so let me take a little time asking it in another way so that we can be clear about what is at stake.

According to the Two-Source Theory, Matthew and Luke are both independently using Mark and Q. We have access to Mark, so we have an idea what Matthew and Luke look like when they are working from a shared source. We know the degree of verbatim agreement to expect. Our question, then, is whether the degree of verbatim agreement is similar when they are using Q. In his recent ETL article, Kloppenborg reproduces a chart from Charles E. Carlston and Dennis Norlin, "Once More -- Statistics and Q", HTR 64 (1971): 59-78 (71):

Triple Tradition Matt Luke Avg. Double Tradition Matt Luke Avg.
Narrative 50.2% 46.9% 48.5%
55.7% 51.8% 53.7%
Words of Jesus 63.5% 68.3% 65.8%
69.5% 73.6% 71.5%
Misc. words 56.7% 60.6% 58.5%
87.5% 80.9% 84.1%
Average 56.0% 56.0%56.0%
69.8% 72.2%71.0%

For those who find figures instantly off-putting, let me express this in words. Matthew and Luke show consistently higher degrees of verbatim agreement in double tradition than they do in triple tradition. One cannot say in response to this, "But this is because double tradition is primarily sayings material" because the pattern is the same with respect to triple tradition sayings vs. double tradition sayings as it is with respect to triple tradition narrative vs. double tradition narrative and so on. Carlston and Norlin sum this up by noting that "the use of 'Q' is even more conservative than the use of Mark, possibly something like 27 per cent. more conservative" (Carlston and Norlin, 1971, 77). This is an anomaly on the Two-Source Theory. Why should Matthew and Luke apparently be so much more conservative in their use of Q, not least given their known respect for Mark's order?

The point of interest here is that the statistics make sense on the assumption that Luke is borrowing directly from Matthew in the double tradition (and Mark-Q overlap) material. They cohere with a scenario in which the double tradition is due to direct borrowing, Matthew to Luke, rather than mutual use of a shared source.

James Robinson once hinted that the all important clues to Q's existence might show up early in the document. I think Robinson was right. The remarkably high degree of verbatim agreement that shows up right at the beginning of Q is an important clue to the identity of the material as a whole. Here, as often elsewhere in Matthew and Luke, the agreement points to direct borrowing by Luke from Matthew, and not mediation via an unknown, hypothetical source.

Note: Carlston and Norlin's figures were criticized by Sharon Lea Mattila and subsequently revised downwards by them, but with the same relative degrees of agreement. Moreover, Carlston and Norlin noted that the same observations hold true with respect to the figures produced by Honore in 1968. (The issue relates to how one counts. Does one count only identical lexical forms, in the same number, case etc.? Can one count synonyms, etc.?). Mattila's 2004 article further criticizes the Carlston and Norlin case, but there are some difficulties with Mattila's re-count which I hope to outline on another occasion.