Lydia formulates the "naturalistic induction" as follows.
Most problems which were unexplained by science in purely naturalistic terms have now been explained by science in purely naturalistic terms. So, by direct induction, any alleged evidence against naturalism has a scientific explanation in purely naturalistic terms.
Science has made and continues to make such great progress throughout history, gradually whittling away at the set of things that were previously not scientifically understood, that whatever it is that you are presently bringing forth as evidence against naturalism, I am sure that science will eventually get to that in time and explain it, as well, as entirely the product of natural causes.
And then she argues that this induction is not going to work. And this refers to the Balfour quote she references.