(Posted here because it fits with the topic of the history of textual transmission and sources, which seems to be the best fit for the forum.)
Sources:
http://www.markgoodacre.org/Q/monopoly.htm (Mark Goodacre)
http://www.markgoodacre.org/Q/goulder.htm (Michael Goulder)
The Case against Q by Mark Goodacre
https://www.richardcarrier.info/archives/12352 (Richard Carrier)
"On Dispensing with Q" by Austin Farrer
According to Wikipedia, "The Q source (also called Q document, Q Gospel, or Q from German: Quelle, meaning "source") is a hypothetical 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. According to this hypothesis, this material was drawn from the early Church's oral gospel traditions."
The above diagram depicts the typical Q explanation for the gospels. Mark wrote his own gospel using his own unique content. Q also contains its own unique content. Matthew and Luke both used Mark and Q, as well as their own source. But neither Matthew nor Luke used each other, and likely they were unaware of each other.
Dr. Carrier explains the hypothesis of Q, "Everything Matthew and Luke share with Mark came from Mark; everything they share with each other came from Q; and everything they share with no one came from yet other lost hypothetical sources: called M, for the material unique to Matthew; and L, for the material unique to Luke."
The first problem is that the theory assumes that M and L are not just material taken from Q by one rather than both subsequent authors. In other words, Matthew and Luke both omitted some content from Mark, so they likely also omitted content from Q, if it did exist. So looking at the diagram above, the green (M) and cyan (L) could possibly have actually come from different parts of Q. Matthew may have omitted half of Q, and Luke omitted the other half.
But what if Q was just an expansion of Mark, a later edit and revision that added lots of new content? All the evidence for Q supports the idea that it was a redaction of Mark, which added a lot of new material, expanding things and removing other content.
In other words, Q sounds just like Matthew. It almost certainly is Matthew, and thus no Q exists at all.
The Farrer hypothesis, which I've just presented, is far simpler than Q. Rather than postulating an unknown source, it simply says that Matthew added to and edited Mark, and that Luke then used Mark and Matthew, expanding upon and editing both. A helpful diagram is as follows:
Q explains how Matthew and Luke got their common material if they did not know of each other's gospels. But this assumes that they did not know of each other's gospels, when they most likely did (or, well, Luke knew of Matthew, since Matthew was written roughly a decade before Luke). Thus, if Luke had read Matthew, Q becomes irrelevant. In addition, we have no evidence from early Christian writings that Q ever existed.
Furthermore, attempts have been made to reconstruct Q, but they don't fit with the theory. It was thought to be a "sayings gospel", but the problem is that the common parts include include a birth narrative (albeit with major differences), a story about John the Baptist, Jesus' baptism and temptation in the wilderness, and his healing of a centurion's servant - but they do not include an account of Jesus' death and resurrection, which makes no sense. Q, if it existed, would almost certainly have included such an account, just as all other early Christian writings emphasized his death and resurrection.
At some points, both Matthew and Luke make small changes to Mark, and agree, in what is known as a double tradition. But if Luke did not know of Matthew, and if Luke only used Mark and Q, this agreement is difficult to explain.
Sources:
http://www.markgoodacre.org/Q/monopoly.htm (Mark Goodacre)
http://www.markgoodacre.org/Q/goulder.htm (Michael Goulder)
The Case against Q by Mark Goodacre
https://www.richardcarrier.info/archives/12352 (Richard Carrier)
"On Dispensing with Q" by Austin Farrer
According to Wikipedia, "The Q source (also called Q document, Q Gospel, or Q from German: Quelle, meaning "source") is a hypothetical 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. According to this hypothesis, this material was drawn from the early Church's oral gospel traditions."
The above diagram depicts the typical Q explanation for the gospels. Mark wrote his own gospel using his own unique content. Q also contains its own unique content. Matthew and Luke both used Mark and Q, as well as their own source. But neither Matthew nor Luke used each other, and likely they were unaware of each other.
Dr. Carrier explains the hypothesis of Q, "Everything Matthew and Luke share with Mark came from Mark; everything they share with each other came from Q; and everything they share with no one came from yet other lost hypothetical sources: called M, for the material unique to Matthew; and L, for the material unique to Luke."
The first problem is that the theory assumes that M and L are not just material taken from Q by one rather than both subsequent authors. In other words, Matthew and Luke both omitted some content from Mark, so they likely also omitted content from Q, if it did exist. So looking at the diagram above, the green (M) and cyan (L) could possibly have actually come from different parts of Q. Matthew may have omitted half of Q, and Luke omitted the other half.
But what if Q was just an expansion of Mark, a later edit and revision that added lots of new content? All the evidence for Q supports the idea that it was a redaction of Mark, which added a lot of new material, expanding things and removing other content.
In other words, Q sounds just like Matthew. It almost certainly is Matthew, and thus no Q exists at all.
The Farrer hypothesis, which I've just presented, is far simpler than Q. Rather than postulating an unknown source, it simply says that Matthew added to and edited Mark, and that Luke then used Mark and Matthew, expanding upon and editing both. A helpful diagram is as follows:
Q explains how Matthew and Luke got their common material if they did not know of each other's gospels. But this assumes that they did not know of each other's gospels, when they most likely did (or, well, Luke knew of Matthew, since Matthew was written roughly a decade before Luke). Thus, if Luke had read Matthew, Q becomes irrelevant. In addition, we have no evidence from early Christian writings that Q ever existed.
Furthermore, attempts have been made to reconstruct Q, but they don't fit with the theory. It was thought to be a "sayings gospel", but the problem is that the common parts include include a birth narrative (albeit with major differences), a story about John the Baptist, Jesus' baptism and temptation in the wilderness, and his healing of a centurion's servant - but they do not include an account of Jesus' death and resurrection, which makes no sense. Q, if it existed, would almost certainly have included such an account, just as all other early Christian writings emphasized his death and resurrection.
At some points, both Matthew and Luke make small changes to Mark, and agree, in what is known as a double tradition. But if Luke did not know of Matthew, and if Luke only used Mark and Q, this agreement is difficult to explain.
