Current disputes over the nature and purpose of the university are rooted in a philosophical divide between theory and practice. Academics often defend the concept of a university devoted to purely theoretical activities. Politicians and wider society tend to argue that the university should take on more practical concerns. I critique two typical defenses of the theoretical concept—one historical and one based on the value of pure research—and show that neither the theoretical nor the practical concept of a university accommodates all the important goals expected of university research and teaching. Using the classical pragmatist argument against a sharp division between theory and practice, I show how we can move beyond the debate between the theoretical and practical concepts of a university, while maintaining a place for pure and applied research, liberal and vocational education, and social impact through both economic applications and criticism aimed at promoting social justice.