Advanced by Dennis R. MacDonald, the Q+/Papias hypothesis (Q+/PapH) offers an alternative solution to the synoptic problem. MacDonald prefers to call this expanded version of Q Logoi of Jesus, which is supposed to have been its original title.
The Q+/PapH has similarities to previous solutions to the synoptic problem. Like the two-document hypothesis, the Q+/PapH affirms that both Matthew and Luke have used a Q document. Like the Farrer hypothesis, it affirms that Matthew used Mark and that Luke used both Mark and Matthew. Like the Modified Two-Document Hypothesis, it affirms that Mark also used the Q document.
Reconstructing the Logoi of Jesus (Q+)
Primitivity
When two or more texts contain parallel content, the Q+/Papias hypothesis uses the following criteria to determine which version is more primitive: An independent version is more primitive than one within a narrative context A unified version is more primitive than one that appears in multiple contexts When a saying relies on a biblical text, a version which is closer to the antecedent text is more primitive than one which obfuscates the relationship A version that exhibits awkwardness is more primitive than one that seems to have been improved A version that is pithy and balanced is more primitive than one containing explications A version exhibiting the redactional qualities of its host text is less primitive than one that is atypical within its host text When the decision of primitivity alternates between different texts (instead of one text always exhibiting a more primitive version), this situation allows for the possibility that the texts in question must have used another, earlier document. In the case of the Synoptics, the Q+/PapH suggests that this earlier text is the Logoi of Jesus (Q+).
Matthew's Minimal Q (MQ-) In order to reconstruct the Logoi of Jesus (Q+), the Q+/Papias hypothesis begins by establishing a minimal version of Q used by Matthew (MQ-). MQ- can be reconstructed by reference to only Matthew and Mark because of two considerations: Matthew contains a number of doublets (two tellings of the same story) which is presumably the result of Matthew taking one from Q and one from Mark. Sometimes the version Matthew takes from Q meets the criteria for primitivity against Mark's and appear to have even served as a source for Mark's version. There exist non-doublets in Matthew (instances where Matthew could have included Mark's account but does not do so, presumably because Matthew found the non-Markan version preferable and sufficient). The cases of inverted priority - that is, when the content of a latter Gospel (Matthew) is deemed to be more primitive than the content of an earlier Gospel (Mark) - are the impetus for believing that Matthew and Mark used a Q document.
Matthew's Expanded Q (MQ+) The next step according to the Q+/Papias hypothesis is to expand Matthew's Q (MQ+). According to MacDonald, "There is no reason to think that Matthew relied on a second source only in these cases of doublets and nondoublets."
The three types of logia used to expand MQ- into MQ+ are: Logia in Matthew that are deemed to be more primitive than the corresponding logia in Mark Logia in Matthew that may reflect the material upon which Mark has performed a secondary redaction Logia that appear in Matthew but not in Mark
The Q+/PapH uses four criteria to determine whether a logion should be included in MQ+: Criterion A - Inverted Priority: The logion in Matthew exhibits a more primitive quality than the corresponding logion in Mark. This criterion can be applied in the cases of the first two types of logia. Criterion B - Evidence of Tradition: The logion in Matthew exhibits evidence that Matthew inherited it. Criterion C - Congruence with Minimal MQ: The logion in Matthew coheres with other logia identified as belonging to Matthew's pre-Markan source via Criterion A. Criterion D - Explanation for Mark's Omission or Transformation: The logion is preserved by Matthew which the interpreter can posit a plausible explanation for why Mark omitted or "radically transformed" it if he would have seen it in Q.
The Logoi of Jesus (Q+) The final step in reconstructing the Logoi of Jesus (Q+) is to bring Luke's Gospel into consideration and to put the logia in order.
The same four criteria used to construct MQ+ are again used for logia from Luke's Gospel (and some from the Acts of the Apostles), with Criterion A, inverted priority, being most pertinent.