A race is a discrete, biologically defined group, no members of which belong to another such group. Members of a race are identified by shared physical characteristics, such as skin color, hair texture, and facial features. Philosophers of science disagree about whether racial categories are biologically significant. People who falsely believe in the moral significance of races, called racists, believe that races are ranked in order of superiority and inferiority based on shared moral and intellectual characteristics that are represented by the shared physical characteristics. They also believe that the shared physical, moral, and intellectual characteristics of a race are inherited from one generation to the next.

Whether or not racial categories are biologically significant, in justice as fairness race plays no role in the public or moral identity of a person. One’s public identity depends exclusively on one’s capacity to have a conception of the good and one’s status as a self-authenticating source of valid claims, which are not affected by race. One’s moral identity depends exclusively on one’s affirmation of the value of political justice and the associations and commitments one makes and withdraws voluntarily. Since membership in a race is involuntary, it plays no role in moral identity. And since race is irrelevant to both public and moral identity, races are morally arbitrary collections of persons.