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The Q source (also called The Sayings Gospel, Q Gospel, Q document(s), or Q; from German: Quelle, meaning "source") is an alleged written collection of primarily Jesus' sayings (λόγια, logia). Q is part of the common material found in the Gospels of Matthew and Luke but not in the Gospel of Mark.
The four-document hypothesis or four-source hypothesis is an explanation for the relationship between the three Gospels of Matthew, Mark, and Luke.It posits that there were at least four sources to the Gospel of Matthew and the Gospel of Luke: the Gospel of Mark and three lost sources (Q, M, and L).
In summary, the two-source hypothesis proposes that Matthew and Luke used Mark for its narrative material as well as for the basic structural outline of chronology of Jesus' life; and that Matthew and Luke use a second source, Q (from German Quelle, "source"), not extant, for the sayings (logia) found in both of them but not in Mark.
A hybrid of these two hypotheses is the three-source hypothesis, which posits three sources for Luke: Mark, Q, and Matthew. 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.
Griesbach (1745–1812), to whom this source hypothesis was first accredited, alluded to his conclusion that Matthew wrote the first of the canonical gospels and that Luke, not Mark, made first use of Matthew in composing the second of the canonical gospels in an address celebrating the Easter season at the University of Jena in 1783.
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.
This suggests that Mark was the first gospel to be written, and that it was probably based on a combination of early oral and written material. Matthew and Luke were written at a later time, and relied primarily on two different sources: Mark and a written collection of Jesus's sayings, which has been given the name Q by scholars. This latter ...
The Farrer theory has the advantage of simplicity, as there is no need for hypothetical sources to be created by academics. Instead, advocates of the Farrer theory argue, the Gospel of Mark was used as source material by the author of Matthew. Lastly, Luke used both of the previous gospels as sources for his Gospel. [2]