The Farrer theory (also called the Farrer–Goulder hypothesis and Farrer–Goulder–Goodacre hypothesis) is a possible solution to the synoptic problem. The theory is that the Gospel of Mark was written first, followed by the Gospel of Matthew and then by the Gospel of Luke.
It has mainly been advocated by English biblical scholars. It is named for Austin Farrer, who wrote On Dispensing With Q in 1955, but it has been picked up by other scholars including Michael Goulder and Mark Goodacre.
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.
Farrer set out his argument in an essay "On dispensing with Q". He says that the two source hypothesis, as set out by Dr B H Streeter thirty years earlier, "wholly depends on the incredibility [i.e., disbelief] of St Luke having read St Matthew's book", since otherwise the natural assumption would be that one was dependent on the other, rather than that they were both dependent on a further source.
This assumption could be displaced by, for example, identifying material appearing in both Matthew and Luke that was very different from either of them, which, when extracted, appears to be a work in its own right, with a beginning, middle and end. Neither of these factors are found in Q, as reconstructed by scholars. He also says (writing before the publication of the Gospel of Thomas) that "we have no reason to believe that documents of the Q type were plentiful", which would have made the hypothesis that Matthew and Luke drew on one more likely.
Nor is it obvious, Farrer says, that a book like Q was likely to be produced as a written manual of the teaching of Christ, since the reconstruction of it requires it to also have significant narrative elements interspersed with the teaching, and to have an interest in symbolism from the Old Testament.
Five arguments are given by Streeter for the impossibility of Luke relying on Matthew.
In his 1955 paper On Dispensing with Q, Austin Farrer made the case that if Luke had been acquainted with the gospel of Matthew, there would be no need to postulate a lost Q gospel. Farrer's case rested on the following points: