Appiah was the son of Joseph Appiah, a Ghanaian-born barrister, and Peggy Cripps, daughter of the British statesman Sir Stafford Cripps. He attended Bryanston School and later Clare College, Cambridge, where he earned a Ph.D. in philosophy in 1982. He taught philosophy, African studies, and African American studies at Yale University (1981–86), Cornell University (1986–89), Duke University (1990–91), and Harvard University (1999–2002). In 2002 he joined the University Center for Human Values at Princeton University, where he stayed until moving to New York Universityin 2014.

Appiah’s early writings concerned the philosophy of language. He turned his attention to political and cultural issues in In My Father’s House: Africa in the Philosophy of Culture (1992), a philosophical exploration of the nature of African identity in the West and in an increasingly global culture. In Color Conscious: The Political Morality of Race (1996; with Amy Guttman), Appiah argued that the notion of biological race is conceptually problematic and criticized what he saw as the tendency to overstate the importance of race as a component of individual identity. The Ethics of Identity (2005) critically examined the various notions around which “group” identities have been defined—including race, religion, gender, and sexuality—and considered how group identity may both contribute to and constrain individual freedom.

Appiah’s other books included Experiments in Ethics (2008), The Honor Code: How Moral Revolutions Happen (2010), and the novels Avenging Angel (1991), Nobody Likes Letitia (1994), and Another Death in Venice (1995).