It is hard to deny that that we possess any moral knowledge, and yet it is even harder to explain where this moral knowledge comes from. We know, for instance, that the Holocaust was profoundly immoral, but how do we know this? Many philosophers explain moral knowledge in the same way as perceptual knowledge. On the perceptual model, we acquire moral knowledge without inference based on experiences that represent moral facts. In Deductive Moral Knowledge, Declan Smithies challenges that perceptual model and replaces it with a deductive model, according to which our most basic moral knowledge is based on deductive inference. Smithies argues against Hume's Law, which states that you can never deduce an “ought” from an 'is”. In its place, he defends “the anti-Humean thesis” that we can know moral facts by deducing them from the non-moral facts on which they depend. We can know the moral conclusion that the Holocaust was wrong, for example, by deducing it from the known non-moral premise that it was genocide.The anti-Humean thesis has wide-ranging implications for moral epistemology. It undermines regress arguments for moral skepticism without relying on special moral faculties such as moral perception, intuition or emotion. It supplies a new form of moral rationalism that explains how we can acquire a priori moral knowledge by deducing moral principles from non-moral assumptions in suppositional reasoning. It explains why no one can be justified in holding or acting upon morally repugnant beliefs, such as the belief that genocide is permissible. In addition, it resolves puzzles about the epistemology of moral disagreement, moral testimony, and moral uncertainty.Deductive Moral Knowledge uses recent innovations in general epistemology to illuminate contemporary debates in moral epistemology. In doing so, it advances our understanding of deductive knowledge and a priori knowledge in general, as well as moral knowledge.