Getting the Gospels in order is one of the fundamental issues in the dating the crucial sources in early Christianity. Before attempting to work out whether we can locate the Gospels in any particular decade, there is preliminary work to be done, to see whether we can get them into sequence in relation to one another. The issue is separable into several separate questions, all of them controversial, all of them interesting, (1) the Synoptic Problem, (2) the question of John's knowledge of the Synoptics, (3) the question of Thomas's knowledge of the Synoptics. There are still other additional questions that we could add, like the relationship of the Gospel of Peter or the Didache to the others, but to make the task manageable, at least in an introductory discussion, it is worth focusing on the texts generally regarded in the scholarship as crucial to the task at hand.
Let us begin with the Synoptic Problem. I have written a couple of books on this topic and it is pointless for me to pretend that I am beginning fresh here so let me instead summarize my conclusions and then offer a special illustration of how I think we can stack up the Synoptic Gospels in sequence.
(1) Mark is the first Gospel and it was used as primary source by both Matthew and Luke. The Priority of Mark is rightly the consensus view in Gospel scholarship. Its major contemporary competitor, the Griesbach (Two-Gospel) Hypothesis does not adequately account for much of the Synoptic data, especially the combination of Mark's alleged omissions from and additions to the combined witness of Matthew and Luke, which generate a curious profile for Mark the redactor. (See further The Case Against Q, Chapter 2 and The Synoptic Problem: A Way Through the Maze, Chapters 3-4).
(2) Luke is dependent on Matthew as well as Mark. This theory (the Farrer theory) dispenses with the need to posit a hypothetical document, Q, to explain the extensive verbatim agreement between Matthew and Luke that is not mediated by Mark. This is the thesis of my Case Against Q, summarized also for introductory students in the last chapter of The Synoptic Problem: A Way Through the Maze (see also the Case Against Q website). It is an argument against a major element in what is currently the majority view in Gospels scholarship, the Two-Source Theory, which argues that Matthew and Luke used Mark independently of one another, which necessitates Q. Arguments for Luke's independence of Matthew are unconvincing, and evidence of Luke's familiarity with Matthew needs to be taken seriously. To take just one area, it is commonly said that Luke's re-ordering of Matthew's discourses is inexplicable, but it makes good sense when one pays attention to Luke's redactional habits with respect to Mark, and his narrative habits overall.
The direction Mark > Matthew > Luke can be observed by paying attention to an important but underestimated indicator of the genealogy of documents, the phenomenon of editorial fatigue. I have argued (Fatigue in the Synoptics) that Matthew's and Luke's dependence on Mark, and Luke's dependence on Matthew, can be seen in the way in which each evangelist will, on occasion, begin by making changes to a pericope, only to lapse into the wording of the source as time goes on, creating minor contradictions. Thus we can see Matthew using Mark in the story of the death of John the Baptist (Mark 6.14-29 // Matt 14.1-12), beginning the pericope by changing Mark's Herod "the king" to his own more accurate "Herod the tetrarch", only to lapse into calling him "king", with Mark, half-way through the passage. Moreover, he adjusts the plot of the story. Where in Mark, Herodias wants John killed, Matthew has Herod himself desiring to kill John, but then Matthew retains Mark's notice that Herod grieved John's death.
Luke appears secondary to Mark in the Feeding of the Five Thousand story (Matt 14.13-21 // Mark 6.30-44 // Luke 9.10-17), which he begins by resetting it in "a city called Bethsaida", which causes an inconcinnity when he later repeats, with Mark, "we are in a desert place here" (Luke 9.12).
The same phenomenon of editorial fatigue also shows Luke to be secondary to Matthew. In the Parable of the Talents / Pounds, Luke, who loves the 10:1 ratio, begins with a major change: ten servants, not three; and with one pound each. Yet as the story progresses, Luke gets drawn back to the plot of the Matthean parable, with three servants, "the first", "the second" and "the other". The wording moves steadily closer to Matthew's as the parable progresses.
I offer these brief examples of the phenomenon of fatigue to draw attention to the possibilities for using literary criticism to theorize about the direction of dependence among related documents. What will be of interest next will be to explore the still more vexed questions of the relationships between the Synoptics, John and Thomas.