Recent work in education research and policy studies has been critical of the view that sees education as a fix for social problems. This perspective invites a reconsideration of the relationship between education and society that breaks from the long held instrumental assumptions informing most education theory and policy, wherein education is a means to a fully reconciled society. Drawing on Ernesto Laclau's argument for the impossibility of society, this article considers the ontology of education in light of society's impossibility. Referring to previous work on rhetorics and tropes in education policy and theory, we discuss how 'ontological rhetorics' in the discourse of education create the objects on and through which it operates. By focusing on the ontology of education, we are able to theorize education as more than and different from its role as a means to an end. Expanding the way Laclau and Mouffe use Althusser's notion of overdetermination, we speak of education as beyond and excessive to the demands of the social, making education a tropological register of the social through which we continually encounter the impossibility of society. Rather than being effective means to current forms of political power, education contributes to the production of discursive resources necessary for the construction ofanypolitical entity, for configurations of the political understood as the ontological process of creating the frameworks of social life.