Is the Humean defeated by induction?

Many necessitarians about cause and law (Armstrong, What is a law of nature. Cambridge University Press, Cambridge, 1983; Mumford, Laws in nature. Routledge Studies in Twentieth-Century Philosophy. Routledge, Abingdon, 2004; Bird, Nature's metaphysics: Laws and properties. Oxford University Press, Oxford, 2007) have argued that Humeans are unable to justify their inductive inferences, as Humean laws are nothing but the sum of their instances. In this paper I argue against these necessitarian claims. I show that Armstrong is committed to the explanatory value of Humean laws (in the form of universally quantified statements), and that contra Armstrong, brute regularities often do have genuine explanatory value. I finish with a Humean attempt at a probabilistic justification of induction, but this fails due to its assumption that the proportionality syllogism is justified. Although this attempt fails, I nonetheless show that the Humean is at least as justified in reasoning inductively as Armstrong.