In this paper I reconstruct Spencer (2014)’s argument supporting the conclusion that ‘race’, in its current U.S. meaning, is a rigidly designating proper name for a biologically real entity, specifically for the partition at the K = 5 level of human population structure. Then, I object to the argument by contesting three distinct key assertions in it. First, I contest the assumption that if a term t has a logically inconsistent set of identifying conditions but a robust extension, then it is appropriate to identify the meaning of t as just its referent. Second, I contest the thesis that ‘race’, in its current U.S. meaning, is a rigidly designating proper name for a specific set of five race categories. Third, I contest the thesis that the partition at the K = 5 level of human population structure that Spencer identifies with the human population continental distribution, or ‘the Blumenbach partition’ as Spencer calls it, is biologically real in the sense Spencer needs. If even only one of my objections is convincing, Spencer’s “radical solution to the race problem” is seriously undermined.