Policy debate about whether to maintain public subsidies for higher education has stimulated reconsideration of the public mission of higher education institutions, especially those that provide student places conferring private benefits. If the work of higher education institutions is defined simply as the aggregation of private interests, this evaporates the rationale for higher education institutions as distinctive social foundations with multiple public and private roles. The private benefits could be produced elsewhere. If that is all there is to higher education institutions, they could follow the Tudor monasteries into oblivion. But what is "public" in higher education institutions? What could be "public"? What should be "public"? The paper reviews the main notions of "public" (public goods in economics, public understood as collective good and Habermas' public sphere) noting the contested and politicised environment in which notions of "public" must find purchase. A turn to global public goods offers the most promising strategy for re-grounding the "public" character of higher education.