We can acknowledge the existence of moral truths and moral progress without being committed to moral realism. Rather than defending this claim through the more familiar route of the attempted analysis of the ontological commitments of moral claims, I show how moral belief change for the better shares certain features with theoretical progress in the natural sciences. There is no ‘decision-procedure’ for ethics any more than there is for molecular biology. Yet, the betterness of true theories can be grasped through what I term ‘undirectional narratives’ of progress. And while there are true moral claims and perhaps numerous moral truths yet to be discovered, we should reject currently popular forms of moral realism with bivalence. Some moral claims lend themselves to the construction of fully reversible, bi-directional narratives and are likely neither true nor false.