There is a consensus amongst many South African scholars, activists, human rights advocates, and citizens that South Africa should become a non-racial society. So strong is our collective belief in a non-racial society in the future of South Africa that we have this principle inscribed in the founding provisions of our Constitution. As an ideal, it stands as a guiding principle in the virtues and values promoted in our society. Arguments abound in the literature for why non-racialism is a noble and worthy cause, but little attention is given to the question of if the attainment of such a society is possible. If non-racialism is a state in which we no longer think about race, I argue that such a state is probably not in the future of South Africa. In this article, I ask what should be done if the attainment of such a non-racial society is not possible. Particularly, I ask if the strategy of racial eliminativism is useful in the endeavour towards a more racially just society if racial thinking will persist despite any of our efforts to move past the idea of race.