On Kwame Anthony Appiah's "Race, Culture, Identity: Misunderstood Connections" (1994), Charles Mills's "But What Are You Really?, The Metaphysics of Race" (1998), and Neven Sesardic's "Race: A Social Destruction of a Biological Concept" (2010).
Coleman Hughes rejoins Mark, Seth, and Dylan to differentiate "race" as population genetics uses the term from racial identity. Mills argues that the latter has been historically constructed to track several markers that don't always go together, e.g., parentage vs. skin tone (consider siblings with different skin tones). Race in this sense is real, in that it's a socially established categorization that has real effects on how people are treated and how they see themselves. But conventions like the "one-drop rule" by which in America folks with mixed black-white ancestry are considered black are historically contingent; our racial thinking does not match the biology involved.
Appiah gives a longer, intellectual history of racialist thinking: He sees our current use of the term as faded detritus of the theories of thinkers like Matthew Arnold, Thomas Jefferson, and W.E.B. Dubois, all of whom thought of race as an essence that could be analyzed, for example in talking about how the spirit of a people informs their artworks (this idea perhaps originated with Herder). Appiah thinks that nothing in reality actually corresponds to such a "spirit," and that no biological categories track with our everyday concept of race, so really, races don't exist. We only need talk about them insofar as to understand the historical persecution of "witches," we would need to understand what the foolish persecutors meant by the term.
Sesardic thinks that by arguing only against this essentialist concept of race, Appiah (and many other thinkers in this area) have constructed a straw man. He thinks that philosophers talking about race need to actually look at the current science of population genetics, and that this field actually does find a genetic break-down that approximates the common racial division of Caucasian/African/Indigenous American/Asian. He rejects the common argument that because there is more within-group variation than between-group variation, races aren't biologically real.
In this discussion, we agree with the first two thinkers that the biological argument is rather beside the point, but since Appiah and Mills are still making arguments that involve scientific facts, even if their overall point is social and ethical, work is needed to figure out how exactly to evaluate their arguments and hence the disagreement between them.
Read Appiah's paper online. Read Mills's paper online or buy the book containing it. Read Sesardic's paper online. We also read The Stanford Encyclopedia of Philosophy article section "Do Races Exist? Contemporary Philosophical Debates" by Michael James (2008, updated 2016), but didn't end up talking about it.
Mills picture by Olle Halvars.