According to John D. Norton's Material Theory of Induction, all reasonable inductive inferences are justified in virtue of background knowledge about local uniformities in nature. These local uniformities indicate that our samples are likely to be representative of our target population in our inductions. However, a variety of critics have noted that there are many circumstances in which induction seems to be reasonable, yet such background knowledge is apparently absent. I call such absences ‘the frontiers of science', where background scientific (...) theories do not provide information about such local uniformities. I argue that the Material Theory of Induction can be reconciled with our intuitions in favour of these inductions. I adapt an attempted justification of induction in general, the Combinatoric Justification of Induction, into a more modest rationalisation at the less foundational level that the critics discuss. Subject to a number of conditions, we can extrapolate from large samples using our knowledge of facts about the minimum proportions of representative subsets of finite sets. I also discuss some of Norton's own criticisms of his theory and argue that he is overly pessimistic. I conclude that Norton's theory at least performs well at the frontiers of science. (shrink)