"Moral disagreement is more widespread, more radical and more persistent than disagreement about matters of fact."
I have two main comments to make on this suggestion: the first is that it is almost certainly untrue, and the second is that it is quite certainly irrelevant.
The objection loses much of its plausibility as soon as we insist on comparing the comparable. We are usually invited to contrast our admirably close agreement that there is a glass of water on the table with the depth, vigor and tenacity of our disagreements about capital punishment, abortion, birth control and nuclear disarmament. But this is a game that may be played by two or more players. A sufficient reply in kind is to contrast our general agreement that this child should have an anesthetic with the strength and warmth of the disagreements between cosmologists and radio astronomers about the interpretation of certain radio-astronomical observations. If the moral skeptic then reminds us of Christian Science we can offer him in exchange the Flat Earth Society.
But this is a side issue. Even if it is true that moral disagreement is more acute and more persistent than other forms of disagreement, it does not follow that moral knowledge is impossible. However long and violent a dispute may be, and however few or many heads may be counted on this side or on that, it remains possible that one party to the dispute is right and the others wrong. Galileo was right when he contradicted the cardinals; and so was Wilberforce when he rebuked the slaveowners.
There is a more direct and decisive way of showing the irrelevance of the argument from persistent disagreement. The question of whether a given type of inquiry is objective is the question whether it is logically capable of reaching knowledge, and is therefore an a priori, logical question. The question of how much agreement or disagreement there is between those who actually engage in that inquiry is a question of psychological or sociological fact. It follows that the question about the actual extent of agreement or disagreement has no bearing on the question of the objectivity of the inquiry. If this were not so, the objectivity of every inquiry might wax and wane through the centuries as men become more or less disputatious or more or less proficient in the arts of persuasion.
(Renford Bambrough, "A Proof of the Objectivity of Morals," The American Journal of Jurisprudence 14 : 37-53, at 41-2 [italics in original])
Note from KBJ: With all due respect to Professor Bambrough, this is a travesty. The question is not whether persistent disagreement about moral matters is logically compatible with moral objectivity. Of course it is! For all we know, there are moral values floating in the sky, invisible and, to date, inaccessible to human beings. The question is not about logical possibility; it is about probability. How likely is it that there are objective moral values, given that the greatest minds humanity has produced (from Socrates onward) have spent more than 2,000 years trying desperately to discover them, with no success? There is no more agreement today than there was 2,000 years ago. In fact, there is much more disagreement! The disagreement is not just persistent; it is pervasive. There is disagreement in metaethics; there is disagreement in normative ethical theory; and there is disagreement in practical ethics—on every conceivable topic. There is even disagreement about which method to use in formulating and testing a normative ethical theory! Some philosophers say that intuitions are irrelevant. Some say that they are relevant but not dispositive. Some say that they are dispositive. In my judgment, the probability that there are objective moral values is less than .00001. Yes, that's greater than zero, but not by much.