The argument from undesigned concidences is a little known argument for the historicity of the New Testament. Once popular in the nineteenth century, the argument has more recently been brought to light by Professor Tim McGrew of Western Michigan University. Very simply, the argument shows how incidental details that are left out by one gospel writer are often filled in by another writer to answer questions raised by the first. This provides good evidence to conclude that at numerous points the authors of the gospels were accurately and independently reporting actual events rather than merely copying one another or engaging in creative myth-making.
Here is Professor McGrew’s talk on the subject at First Baptist Church of Kenner:
And here are more recent interviews on the topic that he has given:
The CrossExamined blog also has a good post on the two categories of undesigned coincidences relevant to the historicity of the New Testament. For Professor McGrew’s response to Ed Babinski’s critique of his argument, visit this post on Victor Reppert’s blog.