Moral dilemmas - Situations in which all agent has a moral requirement to do each of two acts but cannot do both - seem to suggest some kind of inconsistency. I argue that the inconsistency fell intuitively is actually a logical inconsistency, and then go oil to show that we can neither deny the existence of moral dilemmas nor give up the deontic principles involved in the deduction of a contradiction, as both our moral judgements and the deontic principles depend on intuitions that form the basis of our morality. Rather than rejecting our intuitions and thus undermining morality, I suggest regarding, moral dilemmas IS Situations in which a contradiction is not only false, but at the same time true. Finally, the view that moral dilemmas are an example of true contradictions - so-called dialetheias - leads to the application of paraconsistent logic to moral judgements.