I first develop an evolutionary biological model of the origins of the human moral apparatus and the sets of moral rules that accompany it. This model is partially confirmed by generating predictions from it that can be tested against findings in moral psychology and other social scientific disciplines. Using both of these empirical sources, I then argue that the structure of moral discourse is such that we should expect some moral disagreements in our society to be intractable. This means that disagreements over moral verdicts will remain after the moral principles of the disputing parties have been subjected to rational scrutiny and all the facts are known that are relevant to whether the situation judged falls under those principles. I suggest that this claim would be falsified by the existence of moral facts that determined the truth of moral judgements.Human beings are the product of evolution. This is true not only of our bodily organs, but of our affective and cognitive capacities, including the capacity to make and be guided by moral judgements. Moral agents are constituted by particular physiologies, and this affects what they want, what they do, and what facts and values they dispute with other agents. Some philosophers claim that these facts make little difference to the normative sphere: that our natural history is irrelevant to our moral duties. It is the goal of this thesis to show its relevance.Consequently, I next argue against moral realism that it is either false or fails to guarantee a resolution to moral disagreements. Finally, I develop a novel biology-based methodology to assist with the criticism and amending of moral rules in cases of moral disagreement. I argue that considerations of the cultural function of rules, and their consequences for the long-term genetic fitness of members of a population may provide further normative guidance. I apply this methodology to the incest taboo, concluding that it is outmoded and should be replaced with more adaptive rules governing sexual abuse and abuses of trust.