Well, there’s really little to no internal evidence in the gospels and Acts which suggest their date - that’s why people disagree on which gospel was written first and when they were written. Acts is really the only work that might give a clue as to its possible date of composition, and even then, it’s a
very shaky clue: its lack of any mention of St. Paul’s death. Now some claim that the reason why Luke did not mention what eventually happened to Paul is because he had not died yet at the time of writing, which would, in turn, put Luke-Acts somewhere before AD 64-67, the traditional date for Paul’s death. And because of the whole issue of the synoptic problem, the date one believes Luke-Acts could have been written would also affect the dates of Matthew and Mark. (John is really the only stand-alone work here.)
However, at the same time I need to point out that the ‘Luke didn’t mention Paul’s death so he would have written it before that happened’ argument is hardly strong - at least, not as strong as some of its proponents make it out to be. Luke could conceivably have other reasons to not write about Paul’s death, even if it had already happened. One theory I personally like points out the fact that Acts is
not a biography or a martyrology of Paul, although Paul is arguably one of the central characters of the book; it is the story of how the gospel spread beyond Judaea. Ending with Paul’s eventual fate would have distracted readers from this; in fact, one could imagine that Luke was aware that Paul was becoming too large a character by the last part of the book, since he shifts focus
away from Paul at the ending (somewhat abruptly) and turns it towards the message he was conveying. In any case, Luke already has Paul where he wanted him - at Rome, the heart of the Empire. It is the message, not the messenger, that is important.
As for Paul’s letters, Romans is not really the first chronologically by the usual estimates - that’s 1 Thessalonians. (The order we see Paul’s letters arranged in our Bibles is based on order of length than chronology; Romans has the most word count, so it comes first.) In fact, Romans would have been one of the later epistles.
Guess what? Our dating of Paul’s letters actually rely more on a reading of Acts, since there’s also not much within the letters themselves that may suggest the exact dates the letters were written either. Take for example Philemon. In that letter, Paul refers to himself as a prisoner, implies that he is in his old age, and asks for a room in Philemon’s house (Colossians 4:9 and 17, which mention an Onesimus and an Archippus, seems to imply that Philemon lived in Colossae - since Paul also mentions people with the same names in the letter).
And here’s the problem: while we know that Paul was imprisoned in Rome toward the end of his life (hence some people think that Philemon could have been written during that time), that was hardly the only time Paul was ever imprisoned. Acts 24 mentions him in prison in Caesarea for two years, not to mention that there could be some circumstantial evidence that he was briefly imprisoned while at Ephesus (1 Corinthians 15:32; 2 Corinthians 1:8-11). On top of that, Paul himself speaks of his many ‘imprisonments’ (2 Corinthians 11:23). So conceivably, Paul could have written the letter during one of these prison periods of his. As for the age thing, Paul was probably already an old man by 1st century standards by the 50s AD, so that’s hardly a helpful clue: he could have easily considered himself ‘old’ when he was in Caesarea in the mid-50s just as when he was at Rome in the 60s. So while some date Philemon during Paul’s Roman imprisonment, there’s nothing to prevent one from thinking that it could have been written while Paul was in Caesarea instead, or in Ephesus, or in some other place where he was imprisoned.
Philemon shows just how little we have in lieu of a self-sustained internal evidence for the dating of Paul’s letters. The best we can say is that the seven undisputed (i.e. the ones whose Pauline authorship is not questioned by most scholars) letters - 1 Thessalonians, Philippians, Galatians, 1-2 Corinthians, Romans, Philemon - were all probably written during the 50s, maybe up to the early 60s (a
very broad time range), mostly based on inferences from Acts. But that’s about it.
I don’t see what that diagram has to do with this topic.
That just shows the percentage of shared material between the three synoptics. Doesn’t have anything about the date.
