The Fallacy of Alternating Agreements

Synoptic Problem: Markan Priority Defies Logic (Part 12/13)

Another Pattern That Proves Nothing

Before we wrap up, we need to deal with an argument for Matthean Priority that, unfortunately, fares no better than editorial fatigue. An observation advanced by proponents of the Two-Gospel Theory is a pattern of agreement with Mark where when Luke agrees with Mark in order, Matthew does not agree. And where Matthew agrees with Mark in order, Luke does not. This occurs, by definition, where all three are not in complete agreement nor complete disagreement. This pattern has been observed to “alternating,” as if Matthew and Luke “take turns” agreeing with Mark. This “striking” pattern seems difficult to explain as occurring by chance. And if it is not chance, why would Matthew and Luke deliberately choose to only follow Mark when the other is not? This has been advanced as some kind of denouement for Matthean priority.¹ And it might very well have been…if it wasn’t fallacious.

Figure 1 — Excerpt from Four Views p. 75

Matthean Priority From Alternating Agreements Is a Non Sequitur

To the extent this observation is offered to prove anything, it’s a fallacy. And it’s one that is exposed with a shockingly simple proof. Starting with the triple tradition and using only cases where there is agreement with Mark (i.e. the “middle term”), it becomes clear that there are only three possibilities:

• a) either unanimous agreement between Matthew, Luke, and Mark
• b) only Luke agreeing with Mark, or
• c) only Matthew agreeing with Mark

Figure 2— Only 3 Options for Agreements With Mark

The alternating agreements argument doesn’t include the case where all 3 disagree in order. It also doesn’t include the minor agreements between Luke and Matthew, which are where Matthew and Luke agree against Mark (when it comes to “order,” Matthew and Luke never agree against Mark in triple tradition. This is expected as will be discussed. When it comes to text/substance, these are referred to as the minor agreements. For simplicity I’ve referred to both as minor agreements, but the logic for “order” remains). In short, it is not possible for there to be anything other than “alternating agreements” where there is agreement in order between Mark and either one of Luke or Matthew and Mark (i.e. agreement that is not unanimous) when these other cases are excluded. Given that, Option A in Figure 2 above is the only possible situation where Matthew and Luke can agree, while also agreeing with Mark. It proves nothing then to say that Mark follows this order 100% of the time. It’s another hidden circularity argument.

This fallacy is backed up empirically. Assuming, for example, Matthean priority (or for that matter any priority), we see 100% agreement in order with Mark any time Matthew and Luke agree in order. In other words, where Matthew and Luke agree, and Mark also has the same story in his Gospel, Mark adheres to this order every single time. Mathematically, nothing else is possible. That is, of course, Option A in Fig. 2 above.

Figure 3 — Various Possibilities of Agreements

This is illustrated further in the Figure 3 above which illustrates all the possible scenarios (excluding complete disagreement). In arguments for alternating agreements, we would would exclude pericopae 2 and 4 which represent double tradition. We’d also exclude pericopae 7, 9, and 10 which are unique tradition, as well the minor agreements like Pericope 8. What we’re left with is exemplified in Figure 4 below. And Mark will agree in order 100% of the time that Luke and Matthew agree with him (pericope 1), and otherwise Mark will only either agree with Matthew or Luke in alternation.

Figure 4 — Agreements Once Solo, Double Tradition, and Minor Agreements Are Removed

In case you were curious, the same observations occur if Mark is first as in Figure 5 below.

Figure 5 — Agreements With Mark First

Beware of Pattern-Based Arguments

As we’ve discussed ad nauseam, one should be very cautious of “patterns” in the Synoptic Gospels as part of any attempt to give any insights as to priority. Pattern analyses such as these are likely to lead to fallacious arguments like this and should be viewed with extreme skepticism if not outright rejected.

For the alternating agreements argument to be compelling at all, one would need to observe substantial, consecutive, uninterrupted patterns of truly alternating agreements, one pericope, then the next, the back again, then the next, etc. Otherwise “close enough” patterns that occur “most of the time” (e.g. Fig. 1 above) are easily explainable by natural occurrence following the logic above.

We’ve now concluded our review. Let’s summarize and wrap-up next (Part 13/13)!

[1]: Four Views, pp. 76-78