We will start with an example from William Paley’s Horae Paulinae, the first work to explore this sort of argument in detail. Paley’s object is to show the numerous correspondences between the Pauline epistles and the book of Acts. The cluster of coincidences begins with two quotations from 1 Corinthians:
What I mean is that each one of you says, “I follow Paul,” or “I follow Apollos,” or “I follow Cephas,” or “I follow Christ.” (1 Corinthians 1:12)
I planted, Apollos watered, but God gave the growth. (1 Corinthians 3:6)
Both of these verses suggest that Apollos had been at Corinth; the second also suggests that Paul had preceded him there. Turning to the book of Acts, we find an explicit discussion of Paul’s travels and a few remarks about Apollos’s life that bear out these implications. After his first visit to Greece, Paul went from Corinth to Ephesus, where he left his companions Priscilla and Aquilla; he returned to Palestine, stopping in Jerusalem, and then went north into Asia Minor (Acts 18:19, 23), ultimately making his way back to Ephesus. It is during the period of these later travels that Apollos comes on the scene, being instructed in Ephesus by Priscilla and Aquilla (Acts 18:26) and passing from them over to Achaia, where “he greatly helped those who through grace had believed” (Acts 18:27). We might have inferred from this alone that Apollos went to Corinth on this trip, but we need not stop here, as we find that Paul came back to Ephesus at the very time that Apollos was in Corinth (Acts 19:1).
There is a further point of coincidence, equally indirect, between this passage of Acts and an expression Paul uses when remonstrating with the Corinthians in his second epistle. “Do we need,” he asks with evident exasperation, “as some do, letters of recommendation to you, or from you?” The question is rhetorical: “You yourselves are our letter of recommendation, written on our hearts, to be known and read by all” (2 Corinthians 3:1-2). As it happens, the book of Acts provides the clue to Paul’s language; for when Apollos, having been instructed by Priscilla and Aquilla, made his own trip to Corinth, “the brothers encouraged him and wrote to the disciples to welcome him” (Acts 18:27).
What should we infer from the way that the book of Acts interlocks with the Corinthian epistles? The examples we have looked at here offer us some evidence that the authors of each were well informed and habitually truthful. That falls short of a demonstration, of course, but all historical evidence falls short of mathematical demonstration. The case is a prima facie one, and it would be strengthened if we found other, similar arguments with respect to these texts. Paley gives a dozen for each of these epistles.
Paley stresses, in the first chapter of the Horae Paulinae, that the indirectness, the evident undesignedness, is what makes these coincidences significant. The information that makes the passages from the epistles interlock with the history is dropped casually and naturally into the narrative. By contrast, although there is a very close verbal parallel between Paul’s description of the last supper in 1 Corinthians 11:24-25 and the words of institution in Luke 22:17-20, this coincidence might easily be explained by the hypothesis that one of the sources copied from the other. That is not to say that either author actually did copy from the other. But when the points of coincidence are too obvious, the correspondence might have been forged after the historical work became well known, or vice versa.
If there were only a small number of undesigned coincidences, we might shrug them off as statistical noise. After all, in a large box of jigsaw puzzle pieces taken at random, one apiece, from many different puzzles, someone searching with great patience might find a few pairs that fit together (more or less) by sheer accident. But when a large number of pieces fit together, sometimes in clusters, the chance explanation rapidly becomes absurd. That is why, to appreciate the force of the argument from undesigned coincidences, we must have the patience to work through multiple examples. But the picture that emerges when we take the time to do this will amply repay us for the labor and study we bestow on the project.