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The Matthean Posteriority hypothesis, also known as the Wilke hypothesis after Christian Gottlob Wilke, is a proposed solution to the synoptic problem, holding that the Gospel of Mark was used as a source by the Gospel of Luke, then both of these were used as sources by the Gospel of Matthew. Thus, it posits Marcan priority and Matthaean ...
The two-gospel theory is more of a conjecture, as it depends on assuming the accounts of the early church of Matthean priority to be correct, despite there being some good scholarly reasons for skepticism, most notably the long time gaps between the creation of the gospels and the earliest surviving accounts of their authors.
The Matthean Posteriority hypothesis is similar to the Farrer hypothesis but has Matthew using Luke as a source (Mark → Luke → Matthew), rather than vice versa. A final hypothesis holds that Matthew and Luke have no literary relationship beyond their dependence on Mark, but rather each supplemented the triple tradition with oral sources.
New attention is also being given (for example, by Robert MacEwen and Alan Garrow) to the Wilke hypothesis of 1838 which, like Farrer, dispenses with Q but ascribes the double tradition to Matthew's direct use of Luke (Matthean Posteriority). Meanwhile, the Augustinian hypothesis has also made a comeback, especially in American scholarship.
M source, which is sometimes referred to as M document, or simply M, comes from the M in "Matthean material". It is a hypothetical textual source for the Gospel of Matthew. M Source is defined as that 'special material' of the Gospel of Matthew that is neither Q source nor Mark.
Thus, like Farrer, Wilke's hypothesis has no need for Q, but it simply reverses the direction of presumed dependence between Matthew and Luke proposed by Farrer. A few other German scholars supported Wilke's hypothesis in the nineteenth century, but in time most came to accept the two-source hypothesis, which remains the dominant theory to this ...
The three-source hypothesis is a candidate solution to the synoptic problem.It combines aspects of the two-source hypothesis and the Farrer hypothesis.It states that the Gospel of Matthew and the Gospel of Luke used the Gospel of Mark and a sayings collection as primary sources, but that the Gospel of Luke also used the Gospel of Matthew as a subsidiary source.
Goulder points to common Matthean phrases such as "brood of vipers", "make fruit", and "cast into the fire" that each appear in Luke only once, in a Q passage. Goulder's conclusion, based on writing styles, is that Matthew is the source for these "Q" sayings. [39]