In preparation for a project I hope to work on in probability theory, I have prepared a partial taxonomy of undesigned coincidences. In the nature of the case, this is not going to be a rigorous taxonomy such as a set of mutually exclusive and jointly exhaustive categories, for two reasons. First, there are fuzzy edges to what we include in the overall category of "undesigned coincidences." Second, sometimes it is somewhat arbitrary whether one includes a coincidence in one category or another, depending (for example) on whether one regards something as an "event" or a "detail," what counts as "the same event," and so forth.
Nonetheless, I think that a classification is useful. For one thing, it's useful for geeky types who have never heard of an undesigned coincidence and aren't satisfied with concrete examples. Some people work better mentally with general descriptions, or at least find them useful in addition to concrete examples.
A classification like this can help someone who has been introduced to the argument with examples only from one category to appreciate other kinds of undesigned coincidences as well.
Another useful thing about classifying undesigned coincidences is that it can draw our attention to what is usually most confirmed by a particular type of coincidence. For epistemological purposes, we want to be thinking about what is confirmed and how much it is confirmed when we use an argument.
So here is my partial taxonomy:
1. Details given in one source confirm an event or fact explicitly told in another source.
2. Two or more different accounts explicitly telling the same general event have details that fit together in a mutually confirming way.
3. Two or more different accounts agree on the core content while differing in non-contradictory details, though those details do not have other ways of fitting together.
4, Different events explicitly told in different accounts explain and hence confirm each other, or one event explains the other.
5. Details of different sources imply some fact, event, or series of events standing behind the statements though not explicitly affirmed in any source.
6. Two or more accounts tell about an event or series of events that are not at first obviously the same event or series but that, upon examination, turn out to be best explained as the same event or series on the basis of the coincidental fitting-together of their incidental details.
Here are biblical examples of each of these. In some cases I am giving only a sketch of each of these here. The more detailed version may be given in my forthcoming book or in a blog post.
1. John explicitly states that Jesus came to Bethany, near Jerusalem, six days before Passover. (John 12:1) Details given in Mark allow us to count these six days, though Mark makes no such statement. (This coincidence is discussed in Hidden in Plain View.) The details confirm the explicit statement that Jesus came to Bethany six days before Passover, and the statement in John confirms the accuracy of Mark in his more point-by-point chronological version of Passion Week.
2. There are quite a number of examples of this second type of undesigned coincidence among the Gospels. In case after case, details mentioned by the Gospel authors surrounding the feeding of the five thousand (the same general event) fit together in mutually explanatory ways. For example, Mark mentions the green grass at the feeding, while John mentions that it occurred around the time of Passover. Details given by John and Luke (especially) of Jesus' meeting with Pilate (description of the same general event) fit together in mutually explanatory ways. For example, Luke mentions that Pilate, after talking to Jesus, says that he considers him innocent of declaring himself a king, despite the fact that, in Luke's account, there is no record that Jesus denies the charge. (Indeed, he answers Pilate's question on the point rather cheekily and may even be affirming that he is a king.) John recounts that Jesus says that his kingdom is not of this world.
3. The accounts in Acts and in II Corinthians of Paul's escape from Damascus (when he was let down in a basket) mention noticeably different details (though they do not contradict each other except in the mind of a Biblical critic) but agree on the core content. In this category, the varying details do not explain each other (as in the previous category), but the variation itself makes it quite unlikely that one account was merely copied from the other, while the agreement means that both accounts confirm the same core content.
4. The influx of gifts after the destruction of Sennacherib's forces explains the full treasure house of Hezekiah. See here.
5. Numerous different passages in all of the Gospels (and one in Acts) imply without stating it that Joseph, the guardian of Jesus, died fairly early on. The Gospel passages would seem to imply that he died before Jesus' ministry began. This probable fact "standing behind" the narratives is apparently taken for granted as a known matter by the authors, who feel no need to stress or even note it. The narratives seem to arise from the fact that they knew Joseph simply was not one of those present in various cases where Jesus' family interacted with him or confronted him. This confirms both the implied fact (Joseph's early death relative to the other events of Jesus' life) and the knowledge and truthfulness of the authors.
6. Paul mentions in I Corinthians and Romans that he is planning to take a journey to collect and transport money for the Christians at Jerusalem. He sketches his approximate itinerary. Acts 19-21 describes in detail Paul's travel plans and eventual travel prior to his being attacked by a mob in Jerusalem. Though Acts never mentions that Paul is taking up a collection for the Christians on this journey, the details of Paul's intentions and travels fit together so minutely with the epistles (including also II Corinthians) that it is extremely likely that these chapters of Acts describe the same journey delineated in the epistles. Yet the correspondences are so indirect as to make it highly unlikely that Acts is based on the epistles at this point.
All six of these categories confirm hypotheses about the sources/witnesses involved: That they knew what they were talking about, that they were truthful, that they were close to the facts, and so forth.
As a very general rule of thumb, categories 1-3 will tend to draw our attention to a single, particular event and tend to confirm the occurrence of that event at least approximately as related and perhaps even as related in its details. Of course this very confirmation of the events by way of the details given in the sources gives us more reason going forward to trust those particular sources. Categories 4-6, because they involve multiple events, each stated in only one source, events that are implied rather than explicitly stated, and so forth, will tend more to draw our attention to the sources and their probable connection to truth, though of course they also confirm the events and details related. It is a rather subtle matter of emphasis.
These categories, of course, arise in our investigation of all sorts of events in daily life, in the newspapers, in history, etc. This is by no means a way of thinking confined to biblical studies. Perhaps connections to daily life and secular events would be a good topic for the comments thread.