Summary (Diversifying Syllabi): There are a variety of possible views about the metaphysical status of racial assignments, which roughly parallel the variety of meta-ethical views in the literature. Most people are realists about race. Those who see that the realist position is wrongheaded often conclude that race is unreal, subjective, or relative. Both of these views are mistaken.
There are seven candidate conditions for racial identification: appearance, ancestry, public awareness of ancestry, self-awareness of ancestry, culture, experience, and self-identification. Consideration of ten cases of “racial transgressives”—in which a person has some of these conditions but not others — push on our intuitions and ultimately show that we ought to conclude that race is a social construction. This view is to be distinguished from relativism, insofar as you can be wrong about what race you are: Thinking does not make it so.
Comment: This article draws parallels between various positions on the nature of race and various positions on the metaphysical status of ethical values (realism, constructivism, nihilism, etc.). The article explains the latter meta-ethical positions quickly and cursorily, so your students might need a primer (Diversifying Syllabi).