 One way of supporting the latter claim is by introducing the idea of logical probability, where logical probability is a measure of the extent to which one proposition supports another (Carnap, 1962, 19–51, esp. 43–7), and then arguing (Tooley, 1977, 690–3, and 1987, 129–37) that when one is dealing with an accidental generalization, the probability that the regularity in question will obtain gets closer and closer to zero, without limit, as the number of potential instances gets larger and larger, and that this is so regardless of how large one’s evidence base is. Is it impossible, then, to justify universal generalizations?  The answer is that if laws are more than mere regularities—and, in particular, if they are second-order relations between universals—then the obtaining of a law, and thus of the corresponding regularity, may have a very high probability upon even quite a small body of evidence. So universal generalizations can be justified, if they obtain in virtue of underlying, governing laws of nature.