From Arthur’s point of view, British schools are “generally regarded as liberal, cosmopolitan, and freethinking.” He says an exit from the European Union could hurt that reputation, making the U.K. and its universities appear close-minded and isolationist. “I think it’s possible that international students would suddenly find the U.K. less attractive.” Not all university leaders feel this way. University of Cambridge Vice Chancellor Sir Leszek Borysiewicz, for instance, tells Fortune he is concerned about how Brexit could depress the flow of students between the U.K. and other EU nations, but he still expects Cambridge to “be a global player.”