The conceptions of equality of opportunity canvassed so far are intended to be components of a theory of justice, but not all of it or even the central core of it. The general idea is that on some unspecified basis, a social hierarchy with superior and inferior positions is justified. The question then arises, on what basis should individuals gain access to superior positions (and be relegated to inferior positions)? Equality of opportunity is proposed as an answer or partial answer to that question. Equality of opportunity for access to superior positions might also be advanced as a condition that must be satisfied (among others) if the social hierarchy itself is to be morally acceptable.