This paper aims to assess the cogency of Hume’s famous argument against testimony for miracles. Hume starts by arguing in favour of a “general Maxim” which involves balancing the strength of the testimony “considered apart and in itself” against the inductive unlikelihood of the reported event. But although this reasoning shows real insight – anticipating what is now known as the “base rate fallacy” – it turns out that such a separation cannot work, and an adequate maxim must inevitably take into account the specific nature of the reported event when evaluating the epistemic strength of the testimony. There is also a deeper problem with Hume’s argument, which arises from his treating a miracle as an extreme example of an inductively unlikely event. For the believer can agree that miracles are inductively unlikely – or even physically impossible – whenever the world is proceeding normally. Where she will differ from Hume is in claiming that divine activity can interfere with the natural order, and can sometimes be identified through its purposive nature. Naturalist philosophers – like Hume – are likely to reject this, but their best argument for doing so comes not from theoretical probabilistic maxims, but from the hopelessly unconvincing track record of miracle reports, combined with the lack of evidence for divine purpose in the world (as revealed so artfully by Hume’s Dialogues).