Moral relativism is the denial of moral universalism: that there is only one true morality. If a morality is a (formal or informal) system of norms for judging choices and actions, policies and character-dispositions, and the like, as morally good or bad, right or wrong, virtuous or vicious—then moral relativism says two things: first, (1) more than one morality is correct, and second, (2) there are different, but equally correct moralities which judge the same act, by the same agent, in the same circumstances, as having opposite moral qualities. That is: there are some acts that are morally right according to one correct morality and morally wrong according to another, equally correct morality.
The proponent of moral relativism need not say that every actual morality is equally correct. Some moralities may be superior to others. This kind of relativism must deploy some set of norms to judge moralities, and (presumably) these norms will not be moral norms themselves. That is, the judgment that one morality is inferior that that another morality is superior is (presumably) not itself a moral judgment.
According to the “pluralistic relativism” of David B. Wong, the truth conditions of a moral judgment (e.g. “It is morally right that Sarah obey her mother in this case”) vary from one morality to the next because the meanings of moral concepts (such as moral rightness) are relative to a morality’s norms specifying, for example, when the value of honoring parents is overridden by values of privacy and autonomy, or vice versa. Since different moralities place more or less relative importance on different values, what it means to have an overriding moral reason for an action is not the same in every correct morality. The moral judgments of parties representing different moralities may be in practical conflict while both being true because each applies a different concept of moral rightness. There are, however, universal constraints on moralities, derived from human nature and from the functions of morality. A culture’s concept of rightness could not be recognized as a proper moral concept if it did not meet these universal constraints.
On Gilbert Harman’s version of moral relativism, the meaning of the moral concepts employed in a moral judgment is determined by an implicit agreement about moral norms between the one issuing the judgment and the agent whose action is being judged. This “pure version” of relativism does not allow moral judgments properly to be made about the actions of an agent who is outside of the judge’s community. In Harman’s view, only those who share the same implicit agreements about moral norms can be in genuine moral disagreement.
The following are some objections that may be raised against moral relativism. (1) Moral relativism makes nonsense of claims of moral improvement: for example, the claim that the dominant American morality of today which recognizes the moral wrongness of slavery is an improvement over the dominant American morality of the 18th century which regarded slavery as morally permissible. (2) Moral relativism cannot make sense of one’s making a moral judgment fallibilistically: that is, sincerely judging something is morally right while acknowledging that one’s judgment may be in error. (3) Moral relativism denies the phenomenon of genuine moral disagreement by relativizing moral truth: when parties disagree, says relativism, each one’s judgment is true relative to her own morality. Yet in real cases of moral disagreement each party judges the other to be mistaken categorically, and not just in error relative to one’s own moral standards. (4) Moral relativism undermines the normative force of morality: why should someone do what even her own community’s moral norms says she ought to do, if it is just as good for her to do what some other morality says she ought to do instead?
 David B. Wong, Natural Moralities, p. xii.
 A theory that embraces the first claim but not the second would be a pluralistic but not a relativistic theory of morality. Suppose one holds that there is a correct deontological moral system and a correct consequentialist moral system, and that there is no rational basis for judging one system to be superior or more correct than the other. If it turns out, however, that there is no practical difference between the two systems: if, that is, exactly the same set of actions is morally right in each system, then this is pluralism without relativism.
 Not every act must be judged to have opposite moral qualities in different moralities. Moralities can be significantly different without being opposed to one another in every moral judgment.
 The cognitive expressivists Simon Blackburn, Mark Timmons, and Terry Horgan, however, seem to say there is no standard for judging another group’s morality that is not itself a moral standard. On this view, it seems difficult to justify the moral standard one applies to the judgment of another’s morality—or, indeed, to justify one’s positive judgment of one’s own morality. But perhaps one’s endorsement or adoption of a morality is not the kind of thing that admits of or requires justification?
 Wong, Natural Moralities, pp. 71-73.
 Wong, Natural Moralities, p. 74, interpreting Gilbert Harman, “Moral Relativism Defended,” Philosophical Review 84 (1975):3-22, and Harman’s contribution to Gilbert Harman and Judith Jarvis Thomson, Moral Relativism and Moral Objectivity (Blackwell, 1996), pp. 32-46.